I completely agree with almost everything you've written except these few lines. Some athletes will leave their gym in a heartbeat if they're not placed on the team they feel they're entitled to be on or if they want to be on a team that might win NCA or Worlds, and they have every right to do so. But many times when this happens, it's not because the athlete was unhappy or because she/he wasn't receiving quality training to begin with. Parents and coaches from mega gyms with 500-2000 athletes and multiple locations might have a harder time understanding the firm rules that coaches from smaller gyms implement. We live in a brand name culture. We are drawn to the most popular brands before we even consider if they're the best fit for us. I'm guilty, too. For instance, when I go sneaker shopping, I know exactly what brand I'm getting before I even look around. I don't care if there are five other brands that are just as good but maybe a bit less popular. I want what everyone else is wearing and I won't compromise. It's a status symbol. You think Adidas, Reebok and New Balance feels threatened by Nike? You bet they do. So if you provide a good service, what is there to fear you ask? Fear people like me who value a logo over anything else, and we're everywhere. We're not always drawn to something because it's a quality product for us; sometimes we just like the way it looks on everyone else.
Tumbling/Stunting at other gyms -- If I were a gym director who puts countless hours and money into training my athletes the way I think is best, I personally would not allow them to attend other open gyms if I began to notice that my training was coming undone because so-and-so from this gym told them to "do it this way." That's not paranoia; that's protection. And if they came back to me in a boot/sling/cast because they weren't being spotted correctly or because they were allowed to throw a skill I would never allow, all bets would be off.
Disclaimer: Despite my perspective, I am still appalled by some coaches' actions. No one should be removed from a team for taking a picture with an athlete from another gym, and no one should be intimidated to stay where they don't want to be.