I know black belts can be issued from large organizations down to a small school. I also realize belts don't always translate to martial arts skills. I am thinking a black belt in Judo is grest since they invented the belt system. Also the Kukkiwon issues black belts which are legit, meaning you need one to compete in Olympic Taekwondo. Since Judo and Taekwondo are Olympic sports their black belts seem more legit? Meaning if you have one of these you can go to any judo club or taekwondo place and hold rank. Are there any other black belt issuing bodies that carry that much weight in their respective arts?
Ranks in martial arts are largely subjective and local to the school in question when you're speaking of karate (I know nothing of Judo or TKD). So legitimacy is not a universal term. Of course, we all think that our own rank is legit, and appropriate. We would not train under a system that we felt was fraudulent, would we?
I hold a 3rd Dan rank in Isshinryu and I've been studying for 16 years. Is my rank 'legit'? I think that would depend upon whom you ask. It was issued by a respected 9th Dan with whom I train (therefore he knows me and my abilities or lack of same). It was recognized by an Isshinryu organization we belong to (one of multiple Isshinryu organizations). Technically my belt would be 'recognized' by any Isshinryu dojo belonging to my organization; there is no such guarantee that it would be recognized if I were to enroll as a student in other Isshinryu dojos - it might, it might not. And speaking honestly, I can tell you that in my own dojo, there are 3rd Dan students who are more qualified than I am to wear this rank. Probably all of them besides myself. My sensei says I'm a 3rd Dan, so I am. But that doesn't mean I fight as well, or do kata as well, or know more than ANY of his other black belts. It means he decided that I met HIS qualifications and he decided to promote me. That's all it means.
You could not take a bunch of 3rd Dan students of the same age and experience and put them in the ring together and expect them to be evenly matched. Some would be much, much, better, and some would be worse. Same if you asked them to do kata, weapons, or teach a class.
And that variability is within ONE STYLE of karate. Now imagine that compounded across hundreds of ryus, and schools unaffiliated with ANY ryu. As you can probably see, it's an impossible task to determine what belts are 'more legit' than others. You simply cannot compare belt to belt, school to school, organization to organization, style to style.
And that's only talking about the institutions that are doing their best to be legitimate schools and organizations. You've also got plenty of schools and organizations that are willing to give you any rank you wish if you pay them enough. I'm not going to name any of them, but many people here know a bunch of them. If a person shows up claiming an eleventy-dozenth degree black belt from one of those organizations, they're not going to get a whole heck of a lot of respect here. Non-martial artists would probably not know the difference.
And then you have the other martial arts...sigh. I understand that for example, a blue belt in BJJ is a very serious customer, not a person you'd want to get angry with you. A blue belt in my school, well...let's just say I'm not going to be worried if one takes a dislike to me. So a black belt in BJJ is serious business. Worthy of respect anywhere, I'm told (and willing to believe, I do not need a lesson). So how do I compare my rank to a BJJ student's rank? I don't think I can.
Ultimately, belts and dan ranks and advanced titles are attempts to list where a student or instructor is in their path in a single discipline, a single school, under a single instructor. Even then they are still open to interpretation and not something you can easily compare. They are recognitions and cues to those who know or care.
Otherwise, they're a bit meaningless; especially for comparison purposes.