It was, originally. It was even more radical in its first incarnation, and at that point was called McCain-Feingold-THOMPSON.
And, Fred was THE guy who shepherded the legislation throught the legislative process.
And the context, according to your own link, is that Fred Thompson convinced the dems to accede to some republican demands to raise hard money limits (and on the Senate floor, Thompson made the point that hard money donations are equivalent to free speech). Again, CFR was a rare lapse of judgement for Thompson, but the story is more ambiguous than you portray.