The current Jagex stance on bans:

"Offences can be appealed once, if your appeal is denied the decision is final." 

However if Jagex has got it wrong and denies your appeal, you are basically out of luck. Jagex employees are human and are capable of making mistakes. But you do not give players the chance to sufficiently discuss the issue at hand.

I am highly disappointed in Jagex's actions, especially for issues that can be cleared for having a more thorough review. Employing bans for rulebreaking is critical in the game and I have tried to assist Jagex in this multiple times via their tipoff email address. However as much it's the role of the players to follow rules, I believe it is Jagex's roles to properly enforce the rules and if the current system fails to do that, it might be time for a change.

Please improve the support for this. Other support options have a way to talk to a Jagex support employee by email. If a player is indeed innocent, give the player a chance to actually prove it.