If those 100 billion true statements were all (or even mostly) useful and better calibrated than my own priors, then I'd be likely to believe you, so yes. On the other hand, if you replace $100,000 with $100,000,000,000, I don't think that would still hold.

I think you found an important caveat, which is that the fact that an agent will benefit from you believing a statement weakens the evidence that the statement is true, to the point that it's literally zero for an agent that you don't trust at all. And if an AI will have a human-like architecture, or even if not, I think that would still hold.