No one above has correctly paraphrased this quote.

The people and corrupt leaders both have their own interests i.e. the masses want to live in freedom, ability to move up the social ladder etc. Corrupt politicians also have their own interests, namely, centralize power and hoard money.

What this quote means is that people in power try and convince the masses that what is good for them (people in control) is also good for the people. 

For example, Egypt is moving their capital away from Cairo. People in power stated their reasoning as trying to depopulate Cairo. This may occur, but this is not the main reason why they are moving the capital. It is so that it will be harder to form protests and hold politicians accountable.