Do you have evidence that talent can be linearized in such a manner that it is possible to tell objectively within 1% how well an intern will fit at the company? Of course you can linearize on test scores or number of publications or something, but is there evidence that these values will translate precisely to job performance? In my experience, such evidence does not exist, so the zero-sum reasoning is fallacious from the start.
In my experience, when looking for people to fill a position, that we end up with some quantity who exceed our requirements, all of whom we'd be happy to hire. The correlation between that quantity and the number of available slots is not strong. Once the candidates cross the "happy to hire" threshold, the decision comes down to what, in retrospect, seem like random factors (if we vaguely think the company might need a certain type of skill later, we might bump up candidates who have that skill, if someone on the team particularly got along well with some candidate that's a plus, etc etc). Evaluating people is not very precise at all.
The line about spending a "huge" amount of effort finding more females seems a bit misogynist on its face. There doesn't seem to be any evidence that it would be a particularly huge expense. If the goal is to have an incoming ratio with 10% more females, it seems that the additional expense could reasonably be only 10%. It also is fallacious to assume that this is a zero-sum equation; that additional 10% (or 50%, or whatever) could be provided solely for that purpose, and would be unavailable otherwise.
Congratulations on successfully trolling the HR representative, though.