Sure, if "et. al." includes the Florida House of Representatives, who tried their damndest to make this "nightmare" scenario a reality.
If every student already has an exam, how would any "dispute" about gender arise? The law is opening the door for medical challenges for student athletes, explicitly so. Routine physicals check people for good general health and normally don't include declarations of gender. Best case scenario is that women (mostly ciswomen) will be denigrated by being demanded by right wing freaks and bullies to produce medical records proving they aren't too manly.
Hand-wave all you like, but penis inspections and blood draws is the logical conclusion for many transphobes.
(Emphasis added)
Start with that thought. That's exactly the key.
Of course, it would begin with an observation that one of the athletes on an opposing team looked a bit too manly to be a "real" girl. So what would happen next? I think the coach who suspected would ask the other student's coach. The coach would either confirm (unlikely) or deny (much more likely) the trans identity.
Now at that point, either the first coach would believe the second coach, or not. Only if the first coach believed that the second coach was covering it up would it go to an actual challenge. And how would that challenge be executed? The challenged athlete's coach would be asked to produce the certificate, which he has on file, showing the existence of a physical exam. And you are right that such exams don't normally include declarations of gender, if you are using the newspeak definition of "gender". However, every darned one of those exams includes a declaration of sex, which is what is at issue here. They will all say, "male" or "female".
And that's it. It's over. And the legislature knew that, which is why they specifically stated that a routine physical could be used as the certification of sex, because they knew that the routine physical exam was already a requirement for participation.
I haven't read through the detail of the law, beyond what you posted, but I think that it's probably written in such a way that the challenged student would usually never even know that a challenge had been made.
And that's why I said get back to me if there's ever a case where a student is subjected to a genital exam. I don't think it will ever happen. You called that "moving the goalposts", but it isn't. It's the core of the law.
If it turns out that it doesn't happen the way I expect it to happen, and the nightmares actually materialize, I'll join you in complaint, but I don't anticipate any genital inspections or blood draws, beyond what is already required as a condition of participation.