Like you, I'm fuzzy on the details as well, but as I recall the accounts Microsoft banned were for those that had modded/hacked 360's - which also were used to create cheats, but more importantly to Microsoft, were being used to remove the copy protection and allow people to play illegally obtained games on their modded/hacked 360s.
Much in the same way that hackers were doing the same thing with the PS3 using Linux, which is likely the reason that support for Linux was limited to only those using system software 3.15 or older... which in turn means those using Linux on their PS3 can't play online, as they won't have the most recent system software... thus preventing them from hacking their games to include cheats.