I was thinking more of the tentative approach that Can I have a word is used for too. Except that when it is me being tentative, I think I would be even more tentative than May and use Could.
I accept the "you're about to be told off approach" but one wouldn't say no to one's boss, for instance.
I still think a flat out no is rude even with the above expectation. You can listen and argue your case if you aren't in the wrong, or you can say sorry if you are.
And if it's someone just being shitty for the hell of it, well chalk it up to experience and avoid them as much as possible.
Bet none of us would say no to a grandchild who asked to have a word. Whether they were grammatical would be irrelevant.
So, my case, as usual, is that "it depends." There is no hard and fast correct or incorrect for cans and mays.