So... this is typical of the way this argument goes.
Many HN readers are essentially "fellow travellers" with Damore. And you agree with him, and with that whitepaper thing he wrote.
But here's the thing: every time this comes up, this is framed, as you do, as a failure of "everyone else" (meaning left-leaning general folks, often women themselves) failing to understand the truth of what he wrote. But what you don't do is actually defend what he wrote.
And that's because what he wrote was really kinda vile. Indeed he didn't say "Women can't be good engineers". He said: "Women at Google aren't good engineers", which is quite frankly no less offensive. Now, sure, sure, his point was that this was because Google's diversity policies were incorrectly boosting these candidates. But that doesn't change what he said.
So... I don't see that the "female engineer" you were talking to really had it that wrong. You're focused on what to her was a minor fact, and while you seem to be oblivious as to why she might find the "correct" interpretation offensive too...
... you aren't. Because you know it's not really that defensible either and don't want to be held to account for Damore's opinions yourself. So you content yourself with what the rest of us view as nitpicking.