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.
That just prevents anyone except miners from messing with the state. One of the nice properties of Bitcoin is that even miners can't magic more coins into existence than allowed by the protocol or spend other people's money. You lose that a little with this kind of fast sync. It's probably worth it from a usability standpoint though.
Miners could mess with very recent state, but if you download enough blocks with full state to be confident of finality for the earliest one, and verify just those transitions, you're still safe.
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.
If you can get hash collisions, then this issue is only one of many and that isn't exclusive to pruned modes. Bitcoin and friends rely pretty heavily throughout on the assumption of no hash collisions.
