Yes, network is secure as long as honest miners control most CPU power of the network. You say that you have to trust honest miners, that's not necessarily true. You would have to trust them if they would "carry" your money, but they're not banks. You trust them your transaction's confirmation, but even if someone had the power to reverse your transaction that is more than 6 blocks deep, he wouldn't use it to reverse anything. He would use it to generate new blocks, because it would be more profitable.