I don't see where GP claims that the idea is wrong: they're simply pointing out that it's a relatively recent distinction, which implies (reasonably, IMHO) that we likely don't understand it very well yet, or that it may ultimately not be a meaningful distinction to draw once we better understand the underlying mechanisms.
Perhaps near-future advances in genetics and neurology will expand our definition of biological sex to explain gender identity. In that case, our current sex vs. gender distinction would simply be another way of saying "we don't understand how this works yet". There's a lot of this "transitional stuff" in science history, where we have credible anecdotal evidence that our previous understanding is wrong but don't yet know how to coherently explain it. (See: Greek attempts to explain the nature of matter; the infamous cholera map by John Snow; etc.)
That doesn't make the "transitional stuff" wrong: an idea doesn't have to have solid theoretical underpinnings to have merit. It does, however, mean we should continue searching for an explanation.