You are not stating your agency because you are directly affiliated with one of the two in question so stop beating around the bush and stop acting tough.
That's a very strange request...
Some of the best instruction I have had was from the smallest agencies and the worst was with the big ones. If stating this hurts your business then it is not my concern.
This is okay... experience matters when forming opinions. But extrapolating your opinion of a few instructors to make generalized statements of entire agencies that are presented as fact is... ridiculous. And it's sad to imagine anyone taking such advice seriously.
Yes. Instructor matters.
I think just about everyone agrees with this. Regardless of what agency, big or small, the instructor is registered with, it is really just the dedication of the instructor, and the interest the instructor has in delivering a course which provides value to the student, that matters. Thank you for coming around.