Cats have domesticated humans because they are curious about many things including their origins, and lacking opposable thumbs to wield the tiny brushes, they never planned on doing paleozoology on their own.
I would assume the data would still be covered by copyright meaning they could use that data and maybe create and sell derivative works, but not just scrape and publish.
Collections of facts are copyrightable. Which is why you can go out and make a map of your local area but you may not copy the data from google maps. You may end up with the exact same data and that is ok because you both copied the same facts but if there is a mistake on google maps (Perhaps placed as a trap) then you can be caught if your map has the same mistake.
Only the creative aspects of those collections of facts are copyrightable. You can definitively copy from Google Maps, just like Feist could copy from Rural; what you can't copy are the aspects of the maps that require creativity.
As for trap streets, they don't help as much as you think; as we've seen, simply showing that copying occurred is not enough. There was a theory that the trap streets - since they were invented, not facts - could themselves be copyrighted, but in Alexandria Drafting Co. v. Amsterdam, the courts said that copying a few trap streets among a bunch of facts was too minimal to be considered infringement.
The linkedin policy you agree to when you sign up indeed leaves you with ownership of content
"We will get your consent if we want to give others the right to publish your content beyond the Services."
But that license to publish would not extend to scrapers, so they would if re-publishing data, be violating copyright - it appears. Probably not for facts "Greg works at Widget Co." or statistics -- but probably for explicitly copying content, photos, etc. So linkedinclone.com (hypothetical) wouldn't be legal, but a service which scraped and reproduced facts would be.