Thank you everybody for your thoughts.
My beliefs on the issue pretty much align with the points you've each raised. If there is a curriculum in place, also having a time-served requirement holds those who train hard, and learn fast back. I do not believe that all students are created equal, and so when it comes to advancement you can't treat them as if they are. If the particular club doesn't have a rank-dependent curriculum than actual rank isn't all that important, but if an individual is barred from advancing further because of the colour of cloth around their waist, then that individual may be wasting their time continuing to train with that specific club.
In any case, the manager of club location 1 is intent on stirring up trouble by making it a huge issue with the club owner. I think it's a little petty, really ridiculous, and misses the point of martial arts entirely. I guess the trouble with teaching at a club you don't own is you get mixed up in politics you have no control over, and you are limited in your expression of how you believe martial arts should be managed and taught.