The word used by the Buddha is "dukkha", not suffering.
Dukkha is (by definition) the pain you experience when things are not how you want them to be, either objectively wrong or subjectively wrong, and you can do nothing to fix it.
For someone you describe, suffering is not wrong, therefore for them it is not dukkha. But any other aspects of life having a character of conflict between "is" and "should" will still be experienced as pain by this person. So liberation from that is still relevant for them.
Of course if they have absolutely no trace of conflict in their mind, then for them there's no dukkha, but what can we say about their environment? Do they have the insight to avoid creating pain in other people? They themselves may see suffering as peace, but does that hold for the others in their life, and if not, what does it tell about them?
Coming back to your question, this relationship between suffering and suchness is one of the key topics of Mahayana. Indeed, if suffering is an inevitable part of the relative life, and we accept the relative in its entirety as a manifestation of the absolute, doesn't it mean we accept suffering, too? And what happens to the painful aspect of suffering when we accept it? Hence the Mahayana's motto, "Samsara is Nirvana".
In short, your question is a valid one and the answer is in Mahayana's concept of the unity of the two truths, the relative and the absolute.