Not quite. The richest actually do the work to keep the system running. They need to stake their claim to the system to validate everyone else's trx. If is in their best interest not to mess up, otherwise they lose their stake in the system.
For a community of technology enthusiasts, it's surprising to see the amount of misconceptions people here have about blockchain, as it pertains to cryptocurrencies, as well as general angst towards a new technology with a ton of future potential.