At some point serious students of the game need to take the onus upon themselves to learn outside of class and use competitions, seminars, instructional videos and whatever other resources they can think of to improve. Besides, what does it mean to be the "best grappler in the gym"? I think we can easily agree that it's not the person who's tapping everyone, right? Afterall, just because I possess the strength and athleticism to tap out everyone in the gym that doesn't make me the best grappler.
We have a brown belt at my gym that is easily in the top ten in the world at his weight class. He took gold at Pan Ams, and lost to the eventual champ in the quarterfinal at Worlds. He regularly beats two of our black belt instructors, and they have not tapped him with any regularity in several months. He's using resources outside of our school to improve, just as you described. His technical knowledge rivals that of either of those instructors, and he's got phenomenal execution because he is both a perfectionist and the hardest working guy at our gym. Is he strong and athletic? Sure, but that's not why he's winning...even our black belts will tell you that.
I can say with confidence that the folks at my gym would understand it if he decided to move on to another gym, one with elite level competitors and some of the most highly regarded coaches in the sport. I wouldn't hold it against him, he has the potential to be the brown belt world champ, and to become a strong black belt competitor as well.
However, we happen to have an outstanding 3rd degree black belt as our shihan, Johnny Lee Smith. Johnny's technical knowledge and understanding of jiu-jitsu is deep enough that he has something to offer even a world class competitor. Yes, this young man has a great deal of loyalty to our school, but he also feels that he has everything he needs to be a world champion right where he is.
Now, say that instead he had started training at a small gym with a purple belt instructor...perhaps one without much drive to improve his own game? Should this guy have surpassed his teammates and instructor, and then struggled to improve and fulfill his potential...strictly out of loyalty?
I don't think someone should change gyms lightly. However, there is a time where it is understandable, and the right move to make for the development of their jiu-jitsu.
Out of curiosity, of the purples on up posting in this forum what role does your instructor play in your development? I find the greatest value my instructor provides is when he points out minute details to moves I'm struggling with or encouraging me to try something else in a certain position. But these nuggets of knowledge occur less and less as I continue to progress and I believe that makes perfect sense.
That's consistent with what I see at my gym. The biggest role instructors play in helping purple/brown/black belts is to help them refine their technique.
