SPV does absolutely check the block headers, which is all you need to do the proof. You can say that transactions could be omitted from the actual block chain, but not that invalid header data could be served that let someone believe they were paid when they were not or some other falsification.
you're talking only about SPV proof of transaction inclusion, not about the other fraud proofs necessary for the version of SPV theorized in bitcoin.pdf
Blocks aren't valid with double spends in them. You are saying the miner makes an invalid block by the rules in order to have a double spend transaction and then mislead the spv client with that information? I'm not making the argument that relay nodes are useless just that their security is being over stated, it catches this particular issue.
