My point wasn't really about having a closed shoot, but since you brought it up, the Corp I used to work for allowed parents in a room with a one way mirror to watch. IMO, tryouts with tens and hundreds of kids around isn't remotely close to the same environment as a photo shoot. Our corp models, many were minors, changed behind screens with adults walking in and out changing out sizes, colors, pinning, taping and helping them get changed quickly. Those models were used to adults reaching in garments and readjusting body parts to get the fit right. Those models were, also, used to the occasional note being tucked in their hand.
As far as Varsity, it's not just them. Many companies, schools, churches, and camps provide opportunities for kids to travel alone with chaperones, I just don't always feel the opportunity outweighs the risks. I'm not passing judgement on these kids or their parents, but I'd want to accompany my kids for something like a photo shoot and I definitely wouldn't be willing to spend thousands for my travel to TX and NY for multiple shoots. Again, I may be the minority and Varsity may get thousands of applicants.