The problem is that you didn't even understand the logic of the arguments here.
Nope, you've misconstrued what they've said. They're saying that SPV users rely on someone to give them a correct copy of the blockchain because SPV clients are not checking the history to validate if what they've received is correct. The theoretical double spend wouldn't be in the actual blockchain that everyone else can see, it would be in the fraudulent copy being given to the SPV user. Read what achow101 said again:
No,
that is cryptographically impossible. You cannot give a "fraudulent copy of the block chain headers" to an SPV user, if that user knows the currently actual block chain headers, in exactly the same way full nodes do.
That isn't what he said, and you know it.