That is nonsense. I don't recall any ban on Arnold Scwarzenegger movies when he was running (twice). There was one playing somewhere nearly every day if his campaigns. The only reason Dick Wolf might threaten to sue is because he is a commie dog who wants Hillary to win.
Schwarzenegger was not working for one particular studio. Thompson is working for one studio NBC. He signs a contract with them. But Thompson is an attorney right? He can probably get out of it somehow.