Am I wrong? Is there some mechanism by which PoS supports chain splits in a robust way?
While I certainly
do not count as a PoS'er by any definition of the term, the simple answer to your question is, bare PoS doesn't have such a mechanism.
There is financial incentive to mine on both chains, which leads to double-spend attacks and all that.
Ethereum has a financial deterrent in that you lose you stake if you try to submit a bad block, but there is actually no criteria deployed to the network yet to judge what is a bad block.