You are some other people have got some facts muddled up.
Jagex introduced a NEW appeal system which replaced the old system. This in turn gave EVERYONE a chance to re-appeal their accounts. For people with RWT and Macro accounts, despite getting an appeal, MOST were denied. Jagex also gave MOST accounts a last chance appeal which was pretty much the same.
People who commited minor offences but were banned for an accumulation of those minor offences were promptly unbanned with the new system. Any new minor offences are now removed after a year from committing the offence.