Lyte has commented several times that bans are approved by the Riot staff, and then audited later to ensure the system's integrity. 'False positives' do exist, because no system is perfect, but the numbers and comments Lyte has given on the subject suggest that these are extremely rare. Like, similar chances to winning the lottery rare.
Even if you do somehow get perma-banned, you typically have to be in the bottom 1% of Toxic players, get several warnings leading up to it, and typically have multiple chances to reform.
TLR - You're not going to get peer banned unless Riot feels like you deserved it, so it's only a danger if you feel like giving them money entitles you to ignore the rules and act like a jackass.