All it would be would be more, "I saw so and so do such and such or heard about this or that," type "proof". And most people outside the clinic topic really don't care about any of that. The only accusation in Floyd's statements that would really damage Lance's reputation is the one about failed test that was covered up. If proof of that exists (and Floyd first has to overcome the fact that Lance didn't even ride the tour of suisse the year Floyd claims he failed a test...), then this will amount to something. Otherwise, it'll all remain on the level of, "It's not cheating if you don't get caught and he 'never failed a test'."
It's just how we all are in euro/american culture. We're given certain rules and we accept that if we get caught breaking those rules, and it is proven in such a way that doesn't violate any of our rights, then we have to pay the consequences. When we agree to live under a rule, we aren't agreeing to never violate that rule. We are only agreeing that if we do happen to get caught violating that rule then we agree to pay the penalty!
So we all go around living our lives breaking the "rules" of business or relationships or law every single day: and as long as we are prepared to pay the penalties if caught, we consider ourselves to still be righteous and living by the overall concept of the rules.
Accusations from neighbors or coworkers and the like don't count. Even self confessions are less than satisfying. People just don't see it as a true rule violation until the body responsible for enforcing those rules actually catches the violator. That's when the rule was actually broken and the penalty must be paid.
But if one was legitimately caught and then tried to bribe their way out of it or used their influence to get out of paying the penalty that we'd have to pay if we were caught, then we get upset. So that "cover up" allegation is the one and only allegation that the public is likely to give a **** about.