I think one other point to make is that in most cases, bans are not generally instigated by an island. There is likely a mod forum where they discuss several "problem" accounts. I'm sure in most cases where a well-known individual was banned, it was due to a history of bad behavior and not just a single incident. Most people only see the final incident and complain that it didn't meet their personal standards for banning.

In reality, the moderators generally ARE the group that checks the bans. There is no need for a third party arbitration council. This is a private forum run by an individual. I could be banned tomorrow for zero reason and there's nothing I can do about it. The fact that people are allowed to voice their disapproval continuously is a testament to the fact that the mods are being just in the vast majority of cases.