You are mistaking cause and effect, I believe. If a government behaves in a way that earns trust, trust increases. If it behaves in a way that earns distrust, trust decreases.
I actually think that widespread perception that the government is corrupt increases corruption. If you think you can bribe an officer of the law, or a judge, then you might try. If an officer or judge believes that it wont' be reported or that nothing will happen because of it, they may ask for a bribe. If Republicans think Democrats are cheating in elections, then Republicans are going to cheat to even the odds.
I actually think that widespread perception that the government is corrupt increases corruption. If you think you can bribe an officer of the law, or a judge, then you might try. If an officer or judge believes that it wont' be reported or that nothing will happen because of it, they may ask for a bribe. If Republicans think Democrats are cheating in elections, then Republicans are going to cheat to even the odds.
Trust, but verify, right?