Hmmm, back when I was on my parents' policy, it came addressed to me, but at their address (well, I lived there back then, too). That was years ago, though, so maybe it's changed.

Like I mentioned before, if they can find someone they can afford without going through their insurance, there's pretty much no way for their parents to find out. That would be the best bet but it sounds like that probably isn't an option based on their comment above.