In general, when a position is non-obvious, a single conversation is nowhere near enough time to convince a rational person that it's very likely to be true.

Oh, the situation is much worse than that. If your claim is empirical, and needs many background claims to even be coherent, then the evidence required may far exceed what any one person could gather. Compare the claim that one gene with a silly name controls the expression of another - consider the amount of evidence needed to justify the jargon in that case.