You don't have to trust the miners. They act as randomly selected notaries to the chain that have provably fronted considerable resources to accurately notarise the transactions in exchange for being paid handsomely (in specie). If they want to lie when they finally have the opportunity to get paid, and subsequently be caught lying because they don't have enough resources to rewrite the chain then they can, but this would be a pretty foolish errand which would still result in the fact you don't have to trust them.

I agree that the current system involving miners is fraught with political implications. But that doesn't mean the system is broken, it just means it needs to be improved (proof of stake, for instance).