In my opinion a certificate mill is an entity that exists to issue rank certificates. If you send the money and some sort of proof of rank, you get the certificate. I think it is interesting that while you think I do not have the right to think your organization is fraudulant, you think that you have the right to judge a person's proof of rank is fraudlant just by looking at it.
An individual school or instructor, or group of school and instructors, may issue rank certificates. If they make no claims otherwise, such as claims of international status based upon a few students in another country, the legitimacy of that rank is determined by the students and their status in their martial arts community. If students are satisfied with the situation, then all is good. However, once the student leaves that school or group of schools, the legitimacy of the rank is determined by the standing of the school and instructor in the martial arts community in general. They may find their rank is practically worthless
I was a black belt for 25 years with one organization and, when I joined Taekwondo America, I had to start over again as a white belt and work my way up the ranks just as everyone else. To be respected by my fellow students and other students in the organization, that is the way it should have been.
Legitimacy is not all inclusive. One may operate a legitimate martial art school but operate a certificate mill on the side. One may have a legitimate martial art organization with strict rank control, but still be a rip-off because of excessive fees and charges.