Huh. after reading further, it does appear to be a 1,2 sigmatropic rearrangement. They should be thermally suprafacial, and are predicted to be spontaneous.
Anyway, I looked into it some more. Results in image below. The soph organic text we use here is Brown/Foote/Iverson. They note two pathways for the dehydration of butene. E2 or E1 (after a hydride shift). But they don't propose a primary carbocation. If that's the real pathway, then D should be incorporated at the primary position
MSU e-text discusses the solvation of neopentyl bromide and also invokes a 1,2-methyl shift... this time only after a primary carbocation has been formed (it's also where the suprafacial sigmatropic rearrangement is discussed).
http://www.cem.msu.edu/~reusch/VirtTxtJml/rearrang.htm#top1It would also make sense that elimination/rehydration wouldn't be the dominant pathway to the internal alkene. That would seem to indicate that controlling the temperature/time of the reaction should favor more terminal alkene, which I don't think anyone's proposing. I think the internal alkene will be the dominant dehydration product in this reaction at all temperatures, especially cool(er) temperatures.