I believe that's an oversimplification. In this context it presents the impression the intention for the rhetorical inquiry is to win a debate, rather than to identify an optimized solution.
If the day a young girl joins the Girl Scouts she straps on a dildo, it doesn't render her an Olympic male weight-lifting Gold medalist.
That is not to entirely dismiss genital configuration.
But in the new millennium there may be more useful indications, testosterone concentration for example.
hint:
One constructive cognition tool to apply here: if you were a parent of one of the non-transitioned competitors, how would you want this issue addressed?
Dropping their pants isn't exactly reliable but, unless they're into genetic testing that would appear to be the only option.
The latest is to take a cheek swab and check for the SRY gene. Of course that sort of testing isn't going to be done at the grade school or high school level (at least not until the competition reaches the national level).