I agree his overconfident tone isn't helping, but let's not assume malevolence.
I think his argument is that the FP rate can be set to a vanishingly small value, and so we can in theory proceed as if it were effectively zero, as we do with hash collisions. This reasoning is false for two reasons: one theoretical, and one practical.
The theoretical reason is that a nonzero FP rate means that as the number of samples approaches infinity, a false-positive is guaranteed to occur (as you rightly point out).
The practical reason is that complex image classifiers do not exhibit what any sane person would consider a "vanishingly small" FP rate, especially given the volume of samples being processed in this case.
I think his argument is that the FP rate can be set to a vanishingly small value, and so we can in theory proceed as if it were effectively zero, as we do with hash collisions. This reasoning is false for two reasons: one theoretical, and one practical.
The theoretical reason is that a nonzero FP rate means that as the number of samples approaches infinity, a false-positive is guaranteed to occur (as you rightly point out).
The practical reason is that complex image classifiers do not exhibit what any sane person would consider a "vanishingly small" FP rate, especially given the volume of samples being processed in this case.