My impression is that SPV nodes cannot be validator nodes for the reason you stated (proof that ETH is securing the chain requires knowledge of blockchain state). With Bitcoin and node can convert to or from a SPV node to a full node (or vise vera) at any time.

SPV nodes can exist with casper but they cannot be validating PoS nodes. SPV peers essentially have to trust validator peers. SPB peers also cannot independently switch from an SPV peer to validator peer at any time (they must gain approval from the P2P validator network to do so).