"Frankly, the mafia exists because some people don't trust the government or outside/remote political power to gain influence on them. So this way corruption allows people to take back things they think are owed to them."

No. Mafia exists because the state is too weak to enforce property rights and personal safety of the citizens, so a local thug (or a band of thugs) take advantage of it. Most people would prefer not to pay the Mafia but they don't want to be shot by mafia thugs.

"As long as people are happy enough, everything is good."

This could be said to justify literally any horrible act.