Of course the governor Rick Snyder can win back the public trust, he has to change his ways and reform his programs so that the Michigan population will see that evolution and change is taking place and he will win back their trust. It can take longer but it is definitely doable.
Michigan Governor Rick Snyder cannot win back public trust after the Flint water crisis. The Flint water crisis has poisoned many people, including children, leaving some with possible brain damage. He cannot win public trust because the Flint water crisis would have been totally avoided if the government had spent a minimal amount of money to treat the water - estimated at $100 per day. Because he knowingly decided not to treat the water, this has negatively impacted the health of many people, so the general public cannot forgive him or trust him in the future.
The water crisis in Flint has reached epic proportions, and because lead contamination can’t be detected with the naked eye, state officials reassured the public the water was safe to drink for months despite mounting evidence that state officials knew of the growing crisis ahead of time. Having said that, I doubt that people will or even should trust the governor again.
Unlike companies that go through a name change or expensive campaign to change public perception, politicians have to admit defeat and step aside. The governor's identity is linked to the crisis and the amount of time it would take him to overhaul his reputation may be longer than the length of his career.