I am an athletic trainer and I wrestled in high school and before for many years. I've seen Vlahos throw that move many times in competition and have never seen him penalized for it. I have seen it called potentially dangerous when he threw it once, which it should be. The big problem I see is that he's never been penalized for it before in high school (that I'm aware of), so he probably didn't think he would be penalized for throwing it again. If he kept the move and used it after he was warned by the official, then he should be penalized. I think it happened too fast for that sequence to ensue.
From a fan standpoint, I immediately turned to the person I was sitting next to and said "Willis better not wrestle tonight if he can't finish this match now--the crowd will go crazy if he does and to many it will look very cowardly". Even though he presumably had an acutely subluxed shoulder (where it pops out and comes right back in), he could have wrestled (in my mind) if the following conditions were met. 1)it's happened before and it's been "controlled" 2)he has no acute symptoms such as tingling, numbness, etc (don't want any nerve damage or other issues). I've let some wrestle even if they've got some fairly considerable pain as long as they have the strength to protect themselves, which was probably checked on the mat. I'm pretty sure he didn't have any imaging done between matches! You'll notice they stuck him in a stabilizing brace for the finals. Even though these help, it certainly doesn't guarantee anything (i've seen them sublux again with these on). I personally don't think the addition of this would sway a Dr. too much in allowing him to wrestle in the finals, but not finish his match with Vlahos. He must have initially displayed considerable pain (which of course is subjective and what many fans are questioning), weakness (which can be tested), and/or other symptoms indicating something more severe. I don't even know if this was his diagnosis for sure, but it's what I heard circulating about after the match. The brace can be used for other problems, too.
All of these things have to be evaluated and a decision made in a minute and a half! If it's never happened to the kid before, sometimes it seems a little worse at first than what it really is. That being said, the shoulder usually feels worse a few hours later than it did right away (if it's his first time). I personally would have told the kid and his coaches after the match that if it's this bad now, it's probably not going to feel much better for the finals (without knowing his history). It certainly didn't look too bad to me in the finals...but there are also so many variables to consider.
I'd say about 90% of the time the coaches will look to the medical professional on hand for their recommendations concerning whether or not the athlete should continue. It looked to me like they consulted the athletic trainer, but I've seen many coaches force their hands on this issue. Hopefully, it was a decision made by careful, professional judgment made between the coaches, medical professionals, and athlete combined. Certainly a difficult, but rightly questionable decision was made in this match.