If I was doing a competitive fight club then I would restrict training with other groups without my permission as well. Here's why. I had student spar with people outside of school. I didn't know these people or the quality of what they do. She had been sparring with them for about 3 months or more without me knowing. One day I saw a video of her sparring with these people and everything became clear to me. I no longer had to wonder why her sparring didn't get any better. I was looking at it on the video. She had picked up bad habits, tactics and strategies by sparring with these people. Then she would try those same things at the school during sparring classes against other students and none of what she tried worked on us. Basically she went outside the school to learn how to out perform those from the Jow Ga school.
I'm not the best fighter nor am I the best instructor, but I hold myself and my teaching to a high standard. I do my best not to train junk. Had the student just had more faith and trusted and the training that we do in the Jow Ga school, then she would have improved. When I first saw the video I got really mad because I spent time training her how to use Jow Ga kung fu, only for her to throw out the time I spent helping her by adopting trash from someone less skilled than me. I didn't like it and that's when #14 came to my mind. I now understood. It was like a slap to my face insult. In addition to the insult, she wasted her own time because she didn't improve, she got worse, and suffered physically with injuries because techniques were wrong. She was doing things that I constantly remind students not to do in regards to stance and addressing the lead hand.
After I calmed down, I told her that she shouldn't spar outside of the school because she had picked up bad habits that were degrading her Jow Ga training.
If I'm doing competition, then I would simply state the rule so that I can ensure that my fighters will always have something that new for their opponent to deal with. I would want to keep that tree of strategy as fresh as possible.
I don't train sport so the "don't train with another school without my permission" doesn't bother me as long as the student finds a school of quality. "Don't be bringing crap back to the Jow Ga School and having me correct that stupid sheeetz." If a students goes to another school to spar, train, or compete with, then that students needs to go in Jow Ga and come back Jow Ga. If I know a school has good quality training and sparring then I don't have to correct things because I know they will be bringing good habits back.
My Sifu was like this too. My school was only allowed to spar with certain schools. Other schools we weren't allowed to spar with. It had nothing to do with the system, but the quality of the teacher.