I get your point. But I can also see it being a little more complicated than this. Suppose, for instance, you advertised on your website "I'm Spide the instructor, and I give lessons at Q-master Billiards." Now Qmaster is a well established billiard place, and you could be benefiting from an implied endorsement of your instruction. Also, if you do a lousy job, Qmaster could get a blemish for it.
For these reasons I can imagine an instructor having a conversation with a room and maybe working something out.
If it's a really popular and highly regarded instructor and a room in need of a little life, I could even imagine a bit of jelly going the other way.
Anyway, it would be good generally if rooms were welcoming to traveling instructors. They bring new ideas and stimulate conversation and get the blood flowing...
Good points......