I think it's ok if you have an 'official' school and some unofficial training. As mentioned before, if you represent more than one school at tournaments it can be a problem. Also, you can't help but befriend those you train with. If you have friends/teammates from two different fighting each other at a tournament it could make for a conflict of interest.
What if Minotauro was on BTT and Chute Box? Then Arona fought Silva again. It would for sure make so problems. That's an extremem example, but you get what I'm saying.
We don't care if people train at more than one gym/school just gives us more people to train with.
While I don't care where my guys train, I'd like to know if they are my students or someone else's.
I had a guy coming in to train at my school for a while several years ago. He was a Brazilian Blue Belt and loved to talk. I never charged him a dime. I figured maybe he would at least spread the word about our school as he was always telling me how much better my teaching was than anyone else's in town.
One day this guy tells me he has been going down to train at a rival school. No big deal to me. This other school was a charter school associated with Gracie and paying big bucks for his name in the window. They were also charging 125 a month and making their people sign long contracts. That's their business, not mine. Right?
Well, this guy tells me that when he goes down to this other school, they have him instruct as he is so much more experienced than anyone there. Now my curiosity is piqued. "What do you teach them?" I asked. "Oh, I just show them what you showed me" was his response.
First of all, they were the competition.
Second, they had the money to support a Gracie association.
Third, they were charging twice what we were.
Fourth, I wasn't charging this guy anything.
Fifth, what I gave this guy, I gave it to him. I didn't care to hear about how he was giving it to another school who was charging big bucks for my instruction.
The guy finally went away. Good riddance.
As far as the armbar is an armbar is an armbar comment; if you say so.
Do you honestly think BJJ is fundamentally different in terms of where u train?