Unfortunately, yes, anyone can get a blackbelt.
True story #1: I'm in a small town. We have a guy here who taught himself MA from BOOKS, granted himself a 7th-Dan, and opened a school! It's really interesting to watch his classes. *cough*
True story #2: My family moved when I was in college, and I started looking for a new school in the area that I felt I could work with. I was a 4th Kup (4 ranks below black) and the instructor himself, while good in form, was mostly interested in the number of trophies that could adorn his front windows. After spending a half hour dissing my old school in front of my dad (which ticked me off, it was a very good school)... then being impressed by my kicks and style in class, he came up to me after that first class and said "Your kicks are great. Tell you what, work with me for 6 months, and I'll give you your blackbelt."
I was kind of rude in my reply, I guess. But I told him I wanted to earn my black, not have it given to me. I finished my month's contract to ensure my little brother's safety, and never came back.
True story #3: Another school. Not the best...but there was one Dan that I could not understand as a blackbelt. He was sloppy, he had no control, his forms were terrible. He had been with the school for 8 years and they had finally just given it to him for perserverance's sake.