Why does a PoS node have to rely on trust, could it not validate the blocs that were produced while it was offline?
Discussion
In PoS the history of the ledger has no unforgeable costliness. The ledger just consists of a series of signed transactions by validators. Anyone can therefore create an infinite number of alternative histories of transactions and there is no way for someone to look at them and independently determine which one is the real history. There is no way to prove who the validators historically were and what transactions they historically signed.
In PoW there is a unforgeable costliness. You habe to expend energy to create an alternative history and if this is rejected by the nodes, your energy and costs are wasted.
I recommend reading this to get a better understanding
https://hugonguyen.medium.com/work-is-timeless-stake-is-not-554c4450ce18