Are you sure they have actually set it up? I have had Facebook tell me about connections which were simply people who I had emailed who didn't actually have an account - I think it's just one way Facebook uses to try and get people to set up accounts, as if you try and connect with them they get a Facebook message (if there is no image associated with the account you have seen then I'd say this was quite likely).
My account is hidden from randomers, and you can also make it unsearchable in the first place.. Even if it is your 14 year old, they can customise posts so that you don't see everything automatically. You could email this person and ask? Or is that too straightforward?
Someone I know has just set up a Facebook account. If I do a search with the name it does not show at all, only two suggestions are made none of them the right person (it is a very unusual name). But if I search with the email address it shows their account. Does it mean they put restrictions on me seeing their account? thanks