What I'm hearing is that universities coast-to-coast should start "researching" Facebook.
You jest, but that is how a well functioning free market would handle this problem, I think. As long as the information about the payments is public (and information being available is an integral part of any free market, which some people seem to miss), then paying would be a losing proposition for Facebook in the long run since there's always another person ready to step and and start looking you'd need to pay off.…
What we have today is how a free market works. The invisible hand always tipping the scales. They would simply find a better way to get the outcome they want, avoiding the issue altogether (something at the federal level, make an example out of a researcher or institution, etc).
The word utopia is used a lot when anything other than capitalism is being talked about, but the free market, which is an integral part of it, definitely takes the win. We have so many "free economies" around demonstrating how much of an utopia this concept is.