Well, that is false, actually.
The ad hominem fallacy does not rely on truth or falsehood of the accusation. If you believed me, and based that belief on some claim of my personal wonderfulness, you would be just as ad hominem fallacious in that as you would be if you disbelieved me by reason of insult. The ad hominem is a fallacious form of reasoning, not merely an erroneous content.
On the other point, check my critique with a mathematician. I've already run it by one of the world experts in this area, so you're welcome to try. See if infinite recursions can increase probabilities if infinite variables are engaged at the same time, and the whole thing is under totally random conditions.
Good luck.