"In the Pali suttas, SN 56.102-113 state those that realise the Four Noble Truth will be 'reborn in the human state' (manussesu paccājāyanti)."
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Assuming we agree with Bodhi translation, let me quote it:
"So too, bhikkhus, those beings are few who, when they pass away as human beings, are reborn among human beings. But those beings are more numerous who, when they pass away as human beings, are reborn in hell. For what reason? Because, bhikkhus, they have not seen the Four Noble Truths."
I don't read that sutta stating that those who realise the Four Noble Truths will be reborn in the human state.
What I read is that the reason why so many people reappear in a bad destinations contrasting with so few who reappear in better ones is because they haven't seen the Four Noble Truths.
Furthermore, to better illustrate a subtleness of logic, consider the following statement:
"So too, those beings are few who, when trying to construct a bridge, successfully construct it. But those beings are more numerous who, when trying to construct a bridge, fail. For what reason? Because they have not obtained a PhD in civil engineering".
The above does not necessarily say that everyone who constructed a bridge (i.e. reappeared in a good destination) necessarily have a PhD in civil engineering (i.e. saw the FNT). It also does not necessarily say that all bridges constructed were constructed by a PhD in civil engineering (i.e. it does not say that all beings who reappeared in human realm saw the FNT).
In the same way, I don't read the Buddha saying that those who see the four noble truths will reappear in the human realm (as stated in the question). And just for completeness, I also don't read the Buddha saying that all those who appear in human realm necessarily saw the Four Noble Truths. In other words, and to be more precise, it does not seem to say that seeing the FNT is a necessary (or necessary and sufficient) requirement for appearing in human (or deva) realm.
Furthermore, the intent of the sutta seems to be to inspire by showing how easy is to reappear in a bad destination, and to take the opportunity to dedicate to the dhamma practice which would be the best bet to reappear in a better destination. It informs that those who see the FNT have something going for them to reappear in human realm or better destinations, like a civil engineering training is a good bet for successfully constructing bridges (but not necessarily a necessary requirement for building one).
"How can this be? How can one single sutta (Cula-Kammavibhanga Sutta) override the doctrine [...]"
It's not the case that a single sutta overrides a doctrine. A few suttas explain that kamma always comes to fruition at some point:
“Bhikkhus, I do not say that there is a termination of volitional kamma that has been done and accumulated so long as one has not experienced its results, and that may be immediately [in this very life], or soon after [in the next rebirth], or after that [on some subsequent occasion].
-- AN 10.218
Some notes on translation of the above here and and here.
MN 135 is also not a single sutta that says something to the effect of not tying deterministically the deed to the rebirth destination. The Maha-Kammavibhanga Sutta is even more emphatic, and fully explains all possibilities of rebirth:
(i) “Now, Ananda, there is the person who has killed living beings here… has had wrong view. And on the dissolution of the body, after death, he reappears in the states of deprivation, in an unhappy destination, in perdition, in hell. But (perhaps) the evil kamma producing his suffering was done by him earlier, or the evil kamma producing his suffering was done by him later, or wrong view was undertaken and completed by him at the time of his death. And that was why, on the dissolution of the body, after death, he reappeared in the states of deprivation, in an unhappy destination, in perdition, in hell. But since he has killed living beings here… has had wrong view, he will feel the result of that here and now, or in his next rebirth, or in some subsequent existence.
(ii) “Now there is the person who has killed living beings here… has had wrong view. And on the dissolution of the body, after death, he reappears in a happy destination, in the heavenly world. But (perhaps) the good kamma producing his happiness was done by him earlier, or the good kamma producing his happiness was done by him later, or right view was undertaken and completed by him at the time of his death. [...]
(iii) “Now there is the person who has abstained from killing living beings here… has had right view. And on the dissolution of the body, after death, he reappears in a happy destination, in the heavenly world. But (perhaps) the good kamma producing his happiness was done by him earlier, or the good kamma producing his happiness was done by him later, or right view was undertaken and completed by him at the time of his death. [...]
(iv) “Now there is the person who has abstained from killing living beings here… has had right view. And on the dissolution of the body, after death, he reappears in the states of deprivation, in an unhappy destination, in perdition, in hell. But (perhaps) the evil kamma producing his suffering was done by him earlier, or the evil kamma producing his suffering was done by him later, or wrong view was undertaken and completed by him at the time of his death.
-- MN 136
The idea that the nature of the result of kamma can be drawn solely based on the deed is contested in suttas such as The Salt Crystal:
“Monks, for anyone who says, ‘In whatever way a person makes kamma, that is how it is experienced,’ there is no living of the holy life, there is no opportunity for the right ending of stress. But for anyone who says, ‘When a person makes kamma to be felt in such & such a way, that is how its result is experienced,’ there is the living of the holy life, there is the opportunity for the right ending of stress.
He goes on to say:
“There is the case where a trifling evil deed done by a certain individual takes him to hell. There is the case where the very same sort of trifling deed done by another individual is experienced in the here & now, and for the most part barely appears for a moment.
“Now, a trifling evil deed done by what sort of individual takes him to hell? There is the case where a certain individual is undeveloped in [contemplating] the body, undeveloped in virtue, undeveloped in mind, undeveloped in discernment: restricted, small-hearted, dwelling with suffering. A trifling evil deed done by this sort of individual takes him to hell.
“Now, a trifling evil deed done by what sort of individual is experienced in the here & now, and for the most part barely appears for a moment? There is the case where a certain individual is developed in [contemplating] the body, developed in virtue, developed in mind, developed in discernment: unrestricted, large-hearted, dwelling with the immeasurable. A trifling evil deed done by this sort of individual is experienced in the here & now, and for the most part barely appears for a moment.
-- An 3.100
In the following passage, the Buddha refutes the idea that "Whatever this person experiences—whether pleasure, pain, or neither-pain-nor-pleasure—all that is caused by what was done in the past.":
“Bhikkhus, there are these three sectarian tenets which, when questioned, interrogated, and cross-examined by the wise, and taken to their conclusion, will eventuate in non-doing. What are the three?
(1) “There are, bhikkhus, some ascetics and brahmins who hold such a doctrine and view as this: ‘Whatever this person experiences—whether pleasure, pain, or neither-pain-nor-pleasure—all that is caused by what was done in the past.’
[...]
(1) “Bhikkhus, I approached those ascetics and brahmins who hold such a doctrine and view as this: ‘Whatever this person experiences—whether pleasure, pain, or neither-pain-nor-pleasure—all that is caused by past deeds,’ and I said to them: ‘Is it true that you venerable ones hold such a doctrine and view?’ When I ask them this, they affirm it. Then I say to them: ‘In such a case, it is due to past deeds that you might destroy life, take what is not given, indulge in sexual activity, speak falsehood, utter divisive speech, speak harshly, indulge in idle chatter; that you might be full of longing, have a mind of ill will, and hold wrong view.’
“Those who fall back on past deeds as the essential truth have no desire to do what should be done and to avoid doing what should not be done, nor do they make an effort in this respect. Since they do not apprehend as true and valid anything that should be done or should not be done, they are muddle-minded, they do not guard themselves, and even the personal designation ‘ascetic’ could not be legitimately applied to them. This was my first legitimate refutation of those ascetics and brahmins who hold such a doctrine and view.
-- AN 3.61
Moreover, some suttas (such as MN 136) give prominent role to right view at the moment of death and to whether consciousness is tied to sensual gratification at the moment of the death, things that seem to exert strong forces that influence the next destination (see the question Last thought before death?).
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Finally, I understand that it's not that a brutal bloody-handed killer of living beings will be reborn here or there. There's no such killer: there's the killing, and there are also all other good & bad deeds performed in the past, and when these deeds come to fruition, to quote the Buddha again in AN 3.61: "When a person makes kamma to be experienced in such & such a way, that is how its result is experienced."