Determining a valid block isn’t the same thing as determining the correct chain. A node validates blocks by staking, but how does the node know it’s validating

Determining a valid block isn’t the same thing as determining the correct chain. A node validates blocks by staking, but how does the node know it’s validating a block on the correct chain? As far as I can tell, PoS projects don’t have a trustless solution to this problem. Imagine a net split, where the network becomes briefly partitioned. Nodes in each partition would keep adding blocks. When the network converges, there would be two conflicting chains. Using proof-of-work the chain with the most work (longest chain) is the valid chain. Another scenario: Using proof-of-stake I can create my own alternative chain easily (if I don’t want stake money I could create new genesis block), and broadcast blocks to nodes that join the network. When those new nodes receive blocks from conflicting chains, which one is correct? From what I understand of Ethereum, new nodes have to choose trusted nodes when they join the network. I wonder, if one is going to consider trust a non-problem, then why stake at all? A network like Nano works the same way, by trusting a quorum of voting nodes, but there’s no staking or inflation, which has the benefit of allowing anyone to participate without the rich getting richer.