This is a very interesting way of looking at things. You are right that people usually blame the influence of money in politics for the corruption that is taking place. After all, if society wasn't so money orientated and driven by capitalism, then the money offered by interest groups wouldn't be of any interest to politicians.
However, we live in the world that we live in, which is extremely capitalist and solely driven by people's desire for money. Therefore, you could indeed argue that perhaps the first step would have to be to remove the corrupting hand of government from society. Power means increased opportunities to make even more money, so people will always strive to get access to power or at least to get close to those in the highest position to be able to play a part in trying to influence them and their decisions for their own financial benefit. As long as this is the case, corruption will always find a place into politics.
However, getting the government's corrupting hand out of society, as you suggest in your question, would still require a totally different mindset of society, as these two are interlinked. Only within a society where politicians really only serve the people and have no interest in money or power will it be possible for politicians not to be corrupt. This, however, is only possible if society itself loses its interest in power and money, as people who become politicians are members of this very society. Therefore, a shift in our society's principles and morals would be required to breed a new type of politician.
Sadly, however, I do not think that our society is ready (or even willing!) to take the first steps in this direction. Until then, both society and politics will remain open to corruption.