I think it's one of those annoying English teacher things: Q: 'Can I go to the toilet?' A: 'I don't know, can you?'
A case of teachers in a position of power thinking they know more than they actually do.
I'm an annoying English teacher thing!
'Can' instead of 'May' doesn't trouble me from a
grammatical perspective--especially not when making a request to somebody you already know pretty well, and for one which it is perfectly reasonable to expect a response in the affirmative, but it does sound rude to my ears when request is to a stranger or in a more formal setting. I realise it is my own weakness, but I cringe inwardly when I hear "Can I get a hot latte?" or whatever. It almost sounds as if you're aggrieved that said drink hasn't been presented on arrival without your having needed to speak. In situations where I do use it and am asking for permission to act, I tend to include an adverbial 'just' ("Can I just use the bathroom for a moment?") and often shift to the past tense ("Could I just...?")
I think linguists label that 'distancing'--and the extreme examples come across as very British. My American friends pissed themselves laughing the first time they heard the expressions "Would you mind terribly if I opened a window?" and "Would you be so kind as to hold this for a moment?" uttered at a hundred miles an hour.
Alas, all such niceties are going the way of the dodo. Increasingly people have one register for all occasions and 'speak as they text'. I had a chap turn up completely out of the blue last week at my work, asking whether I needed to hire another teacher. He wasn't particularly young, but he was younger than me. He walked into my waiting room, wearing a pair of jeans, didn't have any kind of C.V./résumé, and didn't actually introduce himself, shake hands or even state his name before he started blathering. I was busy, so I nodded to my partner. She took my unspoken instruction to get rid of this man as politely as possible.