The described system is basically identical to Bitcoin's pruned mode. It's lot better than geth's fast sync, which trusts your peers to not have messed with the state.
If the incorrect blocks were published on the network, they'd be rejected by other miners, so you don't have to look far back unless (1) there's a sustained 51% attack on the whole network, or (2) you're a very juicy target and a huge miner can take over your internet connection, and you don't notice a large drop in difficulty.