I hear you. My old coach talked about a guy that came in a "shitty purple," and left a good purple. Not the same as passing yourself as a bb, but similar.
Is that fair though? Some people just have lower standards. I've trained at two or three different gyms that almost never passed out blue belts in less than 3 years. The purple belts were training for like 8.
One guy literally said, "it is important to be better than any average practitioner when you get your belt for the honor of the school. If you are not gifted, you will not be belted."
I saw a 3 or 4 stripe white belt in one of these places, with no former grappling experience, catching clean submissions during transitions and chaining sweeps to submissions against someone much larger who also knew what he was doing. He would have been on his way to purple in most other gyms but he hadn't reached the level of maturity that was expected of these guys.
Some people still think that purple belt is mastery and that brown / black are awarded for instruction. If you got your purple belt after 4 years, having obtained a moderate level of fitness working out 4 days a week during that time, you would not likely be on the level of their purple belts. It just isn't likely.
I'm not criticizing the practice of having different standards. I'm just trying to point out that sucking at a belt level compared to someone at a different school doesn't mean you are any level of illegitimate. You got your belt fair and square. If someone wants to strip it to make you train with them, that's fair, but if you are wearing it and no one makes you take it off or leave, I don't see how you can knock their honor.