Hmm... Nope, I usually hear "в четыре ночи", at least among my friends. I'm a night owl by myself, I'm used to falling asleep late (after 2:00), and waking up late, tooSince I have to work with companies in the US. Maybe that explains why
Yes, I did hear some people saying "в четыре утра", but that's a bit strange for me.
However, it's not a reason for arguing. I agree opinions may differ.