I think there were several cases where the Buddha "learned life lessons" from monks's interactions with laypeople -- this is one example.
So far as I know many of the Vinaya rules have an "origin story" in the commentary which explain why/when the rule was enacted.
Also the Udayi Sutta: About Udayin (AN 5.159) says,
"It's not easy to teach the Dhamma to others, Ananda. The Dhamma should be taught to others only when five qualities are established within the person teaching. Which five?
"[1] The Dhamma should be taught with the thought, 'I will speak
step-by-step.'
"[2] The Dhamma should be taught with the thought, 'I will speak
explaining the sequence [of cause & effect].'
"[3] The Dhamma should be taught with the thought, 'I will speak out
of compassion.'
"[4] The Dhamma should be taught with the thought, 'I will speak not
for the purpose of material reward.'
"[5] The Dhamma should be taught with the thought, 'I will speak
without hurting myself or others.'[1]
... where, according to the footnote ...
According to the Commentary, "hurting oneself" means exalting oneself. "Hurting others" means putting other people down.
Perhaps that -- i.e. "exalting oneself and hurting others" -- is applicable to the question i.e. "the attitude they know better".
I expect that probably a monk does indeed or in fact know better -- so if it were "conceit" ...
Māna (Sanskrit, Pali; Tibetan: nga rgyal) is a Buddhist term that may be translated as "pride", "arrogance", or "conceit". It is defined as an inflated mind that makes whatever is suitable, such as wealth or learning, to be the foundation of pride. It creates the basis for disrespecting others and for the occurrence of suffering.
... then I guess it's likely to be "true conceit" as defined here -- i.e. "thinking one is superior when one is superior", if the venerable compares his attainments with laypeople's and vice versa -- which I guess is part of what might make that so difficult.
I'd also like to answer that no, I'm not aware of such a doctrine in the suttas. I gather that generally monks teach if they're invited to and only when the audience shows respect -- but it's difficult to prove this answer, i.e. difficult to "prove a negative".