No tighter a leash than they're currently holding on GD right now... have you seen the #Rekt threads recently, where a player is complaining about their bans or restrictions or whatever, and WookieCookie or someone comes along and posts excerpts from their chat history?
Furthermore, if this actually becomes a problem, they could implement a feature like this to stop it:
Any player posting in the 'Player Behavior' subb-comm who received a punishment recently can now elect to have their chat history in games that they got reported in (essentially, what the tribunal sees) linked to in their post.
This way, if you got punishments that you think weren't justified, and you elect to post your tribunal history information, other people can go read it, see that you actually were toxic, and disregard you. If you don't post your tribunal history, everyone's just going to say "no proof" and ignore you.
On the flip side, if you weren't actually toxic, people can upvote you, the issue can come to Riot's attention, and they can remove the punishment.