As I see it, they don't own the information, they own the database.

For example, they do not own the fact that you are selling a toothbrush. The do own the records on their servers which catalog the fact that you are selling a toothbrush.

Why? Because they are the ones who went to the trouble of gathering and storing those records.

This is somewhat akin to recording a verbal note from a customer in a book, and storing that book in a giant library. Sure, the user owns the information, but that doesn't mean you are obligated to let every Tom, Dick, and Harry come in and use your library how they see fit- it's your library, even though you do not hold the copyright to all the information stored there.

But if you let anybody use your library, and you don't own the copyright to the content, why are you allowed to stop people from snapping photos of the books and posting them on the web? It's one thing if the copyright holders asked you to, but in this case they want as much distribution as they can get.

Craigslist clearly states that they don't own the data. But just because they don't own it doesn't make it public domain - the ownership belongs to the person who created the listing. To be totally free to repost the data you would need to get explicit permission from each owner.

No. I could write something illegal (libelous, inciting a crime, etc) and assign copyright to you without your consent.

Ok, but then I wouldn't later claim ownership of it as Craigslist has (implying they have consented).

Craigslit does not claim ownership. Craiglist claims it has a license. They are completely different things. Craiglist is enforcing its license to the post. Ownership of the post itself is, and always has been, with the original poster.