Speed is less of a factor than endurance in a persistence-hunting scenario where we're much slower than our prey anyway.
I don't know the facts for this specific claim, but the logic is fair. One group can be better suited for endurance without being faster. One group could also be faster on average without having the individual fastest performers. Not only because of cultural factors, but also because the distribution curves might have different shapes for men vs women. There could be greater outliers (top performers) among men even if the average is higher among women in general. It's not necessarily as straightforward as, say, height, where men's distribution curve is almost the same shape as women's, just shifted up a few inches.
I don't have the data to draw any real conclusions, though.
One of the problems looking at athletic records is that it's really just the elite among a self-selected group of enthusiasts, which doesn't tell us a whole lot about what might have been the norm 100,000 years ago, or what might be the norm today if all else were equal between genders. These are not controlled trials.
I've read that the top women outperform the top men in long-distance open-water swimming, supposedly due in part to higher body fat making women more buoyant, helping to regulate body temperature, and providing fuel. This is the first time I've read that women might have an advantage in running, though.
I wish the article provided citations. The reality is probably too complex to fit into a headline or pop-sci writeup.
Women have a higher pain threshold, and may be able to handle long distance endurance better. However, judging by existing tribal groups in Africa who still practice endurance hunting, that really isn't the case so it's probably bullshit.
Can you please show us what connects your data to being a success as an endurance hunter? Because "men hold more records running a specific distance faster than women do" is not in any way an indication of hunting success.
Do you think Olympic target shooters make the best hunters when it comes to guns and bows?
Another factor is, with endurance hunting, you will need to carry the carcass back to home base. So let's take am antelope, which weighs 125 kg. You need the hunters to bring that all back to base, AFTER the multi kilometer hunt is over.