It's most likely licensed by the user to the host (through a ToS), and the host has the ability to use that license to submit takedown notices of their collective database (which is how US copyright law works).
> use that license to submit takedown notices of their collective database (which is how US copyright law works) //
It would be contract law based on the click-wrap/T&Cs of the website wouldn't it? Copyright doesn't cover facts, only their arrangement; ergo as long as he didn't copy the way the content had been presented he would apparently be clear of copyright infringement.
In Europe we have database rights law too, is there an equivalent in the USA?
I don't believe user profiles are going to be considered facts, but creative works. OKCupid's corpus as a whole would be protected as a database, but the individual profiles would not be considered facts.
The individual fields describing the character of the users are surely factual type data, even if fictional they don't amount to creative works. A mugshot (face image) is not likely to be considered sufficiently creative to amount to a work of itself, and that's the most creative component of a persons profile.