HTTPs would work but also if you scroll down a bit and look at the policy JSON (http://pastie.org/private/tkr7iyqzqrezmmqazbfijw), it has an "expiration" field which would mitigate the type of attack outlined in the parent post since after a period of time the signature would no longer be valid.
I suppose that's solved by serving the form over https. Perhaps that's just what I was missing.