The great virtue of valid logic in argument, rather, is that logical argument exposes premises, so that anyone who disagrees with your conclusion has to (a) point out a premise they disagree with or (b) point out an invalid step in reasoning which is strongly liable to generate false statements from true statements.

This is false as a description of how mathematics is done in practice. If I am confronted with a purported theorem and a messy complicated "proof", there are ways I can refute it without either challenging a premise or a specific step.

• If I find a counterexample to the claimed theorem, readers probably won't need to dive into the proof to find a specific misstep.
• if the theorem contradicts some well-established result, it's probably wrong. (This is closely related to the above)
• If a purported proof falls into a pattern of proof that is known not to work, that is also sufficient grounds for rationally dismissing it. (This came up during the discussion of Vinay Deolalikar's purported P != NP proof -- most of the professionals were extremely skeptical once it became clear that the proof didn't seem to evade the known limitations of so-called natural proofs.)