Unless you're going to argue that you own anything you happen to know, even after other people know it? Unless you're going to argue that a posted policy on a free website constitutes a binding agreement?
If that was true in all cases, the story we're commenting on wouldn't exist.
Trying to apply rules made for physical items (if I take it you don't have it any more) to things that act completely differently is a really bad idea.
Would it make a difference if I had said "something akin" to personal information as property? I mean, we're reading this story, so personal information has currency in some way, right? Seems to me that with some political will that the laws can be nudged further in favor of the user.
The FTC is empowered to enforce that with a variety of penalties, including extensive fines.