I don't necessarily have a problem with crying in the gym, it just depends on the kid and the situation. That's just how some kids handle emotion- fear, frustration, pain, disappointment- and I don't think there is anything wrong with that. BUT, they also need to know how to calm themselves, change their perspective, and re-focus. So I think the key is not whether or not they can/should be allowed to cry, but rather helping them develop skills to regain control.
In this situation, the child was probably a mix of scared, upset, disappointed, and embarrassed- in a high stress situation like a meet when you're 11, I think it's totally understandable for that child to respond in an outwardly emotional way. Maybe not to the extent she did with the loud wails and sobbing, but if that's how she typically responds, I wouldn't expect it to be any different at a meet. She needs coping skills.
Ask if she's okay, see if she can tell you what's going on- is she scared, disappointed, etc. Have her take a few breaths and then encourage her to walk to the bathroom or get a drink to get herself together- try to avoid having her teammates get in her face and pester her- that seems to aggravate problems. When she returns, treat her as usual. Maybe just remind her how to move past the upsetting circumstance and refocus her energy on the new task at hand and the factors she can control. And really, once she has that crying outburst, she might be totally fine and ready to move on to the next thing. That's just how some kids (or people) release tension. I remember at one meet as a young teen, I could not make a single skill in beam warm-up. It was disastrous. I was worked up, stressed, terrified, and not a good competitor to begin with. I started crying- not obnoxious or attention drawing- quietly and keeping to myself, coach threatened to scratch me from the event, but I had so much tension built up that needed to come out somehow. I was slightly older than your gymnast, so I was able to calm myself in time and went on to compete the best beam routine of my life. Probably because I had released all of the tension that usually bogged me down on beam during warm-ups. Does that mean I should have had a meltdown before beam at every meet? Absolutely not, but in this particular circumstance- I had an overwhelming amount of feelings built up that needed to be let out somehow and actually letting them out (in the form of tears) proved to be more beneficial than just bottling it up.
This would be a good learning tool for all of your girls, so make sure you talk about it at practice this week. Talk to them about things they can control vs. things they cannot (such as equipment) and that all they can do is focus on what's in their control- remembering their training and corrections and their attitude about the situation.