To be fair, Sandberg saying "we didn't do this" about an illegal thing doesn't necessarily mean that they didn't do this. Also, why would a company much smaller than the others agree to this?
Losing a talented employee can hurt regardless of the size of the company that snaps them up. A larger company will often have more resources with which to compete in the job market. A smaller company might (illegally) join such an agreement for the same reason that a weaker nation might sign a defensive pact with a stronger one.
Right, but as a Googler who went to FB, movement was much more common one way than the other. Also, I can say for a fact that Facebook recruiters were using Google org charts to reach out to people, so that's probably why they didn't agree to this, not because they're super awesome nice people.