You're correct, Ethereum uses account balances. You don't have to keep track of inputs and outputs, just check that the balance is sufficient.

Since each block header has a merkle root of the block's state, you can just get all the block headers to check PoW, get the current state, and validate transactions and states as many blocks back as you feel you need to make sure a miner hasn't faked the current state.

Here's an old article by Vitalik on the subject:

https://blog.ethereum.org/2015/06/26/state-tree-pruning/