Yeah, you are probably right in regards to his rep, but I'm not sure how much actual backing Gotti had in the joint. Sure, he had his rep and his notoriety, but he didn't have any actual mob comrades or organized crime associates in the joint with him at that time. So, it wasn't like when he was out on the streets and he had bodyguards and shooters shadowing him ready to protect him in the event of any kind of attack. In Marion, Gotti was a high-profile inmate basically alone.
And the type of power that Gotti had was the type of power that can be easily revoked under certain circumstances. Gotti's power on the outside was due to his position as boss of a major organized crime family that included many killers and violent men who answered to and performed work for John Gotti. But you take a guy like that and stick him on a desert island with a group of savages, that type of power isn't going to be worth much.
In a case like that, and in a place like Marion federal prison, being physically tough and strong probably holds more weight.
Gotti was simply a middle-aged, out of shape guy surrounded by lowlifes, many of whom were probably tougher and more physical than Gotti ever was.