I am especially not inclined to fix people's arguments when they are wrong either way. Fixing from wrong to still wrong is weird.

Not really, it's a common method for showing that someone is very wrong. It's just the common "But let's suppose we fix that [alternatively, that I spot you that for now] - even then there's still a problem, as..."

Regarding much of the rest of the post: The idea is not to silently reply to a corrected version, but to explicitly note the correction and reply to that! Then people can, rather than just being confused about your correction, actually evaluate your corrected version and verify whether or not it still conforms to their intentions.

As to skipping ahead while smaller issues are still pending, I wonder why you think building on rotten foundations is wise. I think it can work sometimes, but it's a bit ambitious.

Hence you fix those foundations, rather than silently building on top of them.