Probably. Distributions don't necessarily have a huge amount of overlap. For example, upper body strength is also a distribution but the overlap is so small that 95% of men have stronger arms than 95% of women. With something as general as aptitude for things vs people the overlap is probably much greater than that but not certain without more data.
https://qph.cf2.quoracdn.net/main-qimg-51a4b98a4975f1bc2e68c...
https://qph.cf2.quoracdn.net/main-qimg-c76c62e97e58fe9a64a83...
There are female children too.
More than 5% of the male population is old, weak, and/or disabled
There are old, weak, and disabled women as well. Additionally, if you think old men are weak I suspect you have never had to wrestle an eighty year old with dementia out of a bath tub. They are remarkably, irritatingly strong.
I agree, of course, but I believe the wrestling comment did not refer to the methodology used in the research.
We organize our understanding into categories and reason about them using propositions that are either true or false.
However I think the last sentence isn't as true as you make it out to be. I remember seeing statistic couple years back about this very subject and in that data woman had to be in the top 10% of "women who prefer working with things to people" to be as likely to work with things than "men who prefer to work with things to people" and it was pretty much same vice-versa.