Methinks they have cause and effect reversed. It's not that rich greedy people are more likely to be unethical, but that unethical greedy people are more likely to be rich.
. . .
Quod erat demonstrandum:
The rich and powerful, those that shape society in their image, are greedy, self-interested and unethical because those are behaviours that are successful, and those behaviours are successful because that's the way that society is set up... by the previous generation of greedy self-interested and unethical bastards in power.
It's a feedback loop, a vicious cycle, resulting in the concentration of wealth and power in the hands of those who'll use whatever means necessary to get it... and the evolution of a civilisation where honesty and altruism are counter-survival traits. It's limited by the law, but only insofar as they can find loopholes or avoid being caught, or cheat & steal legally... But they also have the power to get the laws changed in their favour as long as thy can con the more honest majority to go along with it.
The logical end point is an amoral ruling elite with enough power and wealth that they are above the law, and no concern for what the powerless subjugated majority think of them.