The commenter more or less admitted that they have no way of knowing that the algorithm is actually correct.

In your first analogy it would be like if text predictors pulled words from a thesaurus instead of a list of common words.

The mersenneforums have users solve an obscure (to a non-mathematician) but relatively simple number theory problem.

I struggle to find something more obnoxious than incorrectly employed formal logic.

There is no contradiction. The intersection of “native-sounding English” and “(English with) no grammatical errors” is not empty. So it’s actually perfectly possible to meet both criteria.

It also wouldn’t be a logical contradiction even if it wasn’t possible, since contradictions are conflicts of arguments that rely on different propositions being true, not the valuation of the actual propositions.