It's not clear from the slides that the companies were "participating" at all. Further Snowden leaks showed that the NSA was cracking large internet companies' internal systems communications. PRISM doesn't necessarily need their cooperation at all.
Either the companies on the PRISM list are willingly collaborating, or NSA bribed one or more employees, or NSA attacked their infrastructure.
If it wasn't willing cooperation, then the PRISM companies have a security breach to solve. None of them have said whether they have such a breach or not.
I wish we had even more technical details.