I suggest that you research the idiom, "he may be X, but Y."
If I say "He may be tall, but he's ugly"[1] his height is not in question. Semantically, it means that one of his features may make him effective at something, but another feature (or aspect of the situation) offsets that effectiveness.
> If I say "He may be tall, but he's ugly"[1] his height is not in question.
The idiom may, depending on context, imply acceptance of the proposition that is preceded by "may", but more generally (whether or not that is the case) it means that that proposition's truth is irrelevant, and that the important thing is the subsequent proposition.
