I believe NFL coin tosses let the coin hit the ground. All methods I know of biasing a coin toss involve catching the coin. As long as the coin hits the ground and bounces at least once, a lot of randomness is re-introduced.

If you can pay off a referee then the coin toss would be the least effective way to do it. A single bad call would gain you a much bigger advantage.

It has far more plausible deniability, however.

Maybe. It only takes one bad call at the right time to throw a game. If the ref is consistently bad and missing call for both sides what is one more bad call?

I don't care much about bad refs so long as they are consistently bad. However a perfect ref who missing one critical call is a lot more suspicious. Of course I prefer a great ref, but I can work with a fairly bad ref.