I'm ok with all you've said except for that minor premise that females were kept close to home for protection. What are they doing there, sorting socks and sweeping trash into neat archaeological sites?
Unless they were heavily pregnant or infirm, the women---and the kids too---were out gathering food, checking the traps, and following other gainful pursuits. Not too many got sneaked up on by any Neandertal, I would think. Probably not stupid enough to go out alone either.
Keeping women home sounds like the practice of an affluent society. Mind you I'm not saying the early hunter-gatherers were down and out; hunter gatherers are very efficient at obtaining food. But the usual picture we get, of menfolks going out and bagging moose while the little women hide in the caves, that's just Hollywood. They probably subsisted on meat less dangerous to catch; any child can trap a squirrel.
Furthermore, I would think that many primitive people, up to modern times, thought nothing of sexual activity with pre-adolescent females. Therefore it should be no surprise if they didn't understand the link between sex and reproduction. What they observed was simply that females make babies, once they reach a certain age. In many cultures those females might have been sexually active for several years. To the primitive mind, what's to say that one male caused a baby to form?
From a rather extensive survey of hunting-gathering peoples, it turns out that women are responsible for about 65% of the calories and the men the rest. The men are mostly responsible for the high-protein meat, though. All of this adds to your point...