Lets be honest, it's rare that these people are ever swayed by facts.
The facts they cite are not what led them to their beliefs. They arrived at their beliefs according to different lines of reasoning (e.g., "Don't ever trust the government") and then try to backfill with arguments that allude to the available facts. Or stated differently, they cherry-pick and misinterpret the facts to support a proposition they believe for wholly different reasons. It wasn't very hard to get Tim to tip his hand and reveal that his claims had more to do with ideology and worldview than with radiation. Toward the end, he wasn't even really trying to hide it. He made the ideology argument his major point.
And did so, as usual, without even really understanding human psychology, either. While I'm quite sure that he would lie and claim that he'd accomplished something he hadn't, I'm also sure that he would gleefully reveal if
one of his rivals had lied to accomplish something it could be proven they hadn't. If you won't accept my argument about Nixon, which I admit is very much armchair psychology from me, there's always the Soviet Union or North Korea. If a retired Navy electrician can find the one thing that proves the lie, the only way to suppose that no other nation had the expertise to show it up is to assume that they could and didn't. So they, too, would have to be in on the hoax. Eventually, everyone is.