The nature of the body high is "entactogenic" meaning "touch within". This means it's the nature of the body high itself and the way it interprets touch that causes this. I don't know the exact mechanism, nor do I believe it's known. I could be wrong, though.
I will say one thing, though. I have hypersensitivity to touch from sensory integration dysfunction, and mdma makes touching things with the palms of my hands bearable. I don't get the intense disgusting tasting synaethesia, either. Textures suddenly taste wonderful and it feels good to touch things. For a period of time after, my sensory integration problems go away. Generally about a week or so. Neat stuff =)