I think that's a very US thing, it's somewhat considered harmful to see those nipples, so they are always censored? Still, I believe many of those music videos are appealing to the men's sexual instinct more than their musical taste, hence if there was any logic, the whole video should be censored and not only the nipples.

Anyway, you should probably be grateful that someone is protecting you from getting a hard one in the dentist's office, the dentist could probably misunderstand that.