I don't find it upsetting so much as potentially awkward. I don't want my kid to go around broadcasting to all of their friends that OH MY GOD YOU GROW HAIR IN WEIRD PLACES TEEHEE. It's something that I've dealt with (on a different issue), and I feel like it varies from kid to kid. Some kids can be trusted not to blather about it to everyone—they get that it's not "private", per se, but that it's something that you don't talk about with everybody—and some can't. With the kids that can't, and the other kids that they were dealing with at the time, it was a personal choice not to disclose that much to them. Saying something like, "It happens to you when you're older" and killing the topic was enough. It might not have been the best way to deal with it, but it worked.

I like your suggestion, though. :)