I'd like to think that even in that situation I'd try to be a little more polite; but yes, phrasing like this would certainly seem less out of place if he and I already knew we had a commitment of some sort to work together to solve his problem.

Hmm. Perhaps the reason this particular misunderstanding grates on me where others don't is that he should be able to figure out that he has no reason to think we have any such pre-existing commitment. Perhaps the difference between this and other more forgivable misunderstandings is that this particular one ought to be trivially resolved by him spending twenty seconds to stop and think, and he hasn't bothered to.