Burkhead's fumble was as he was hit/about to be sacked, on a pass play out of the Wildcat.
I don't look at Rex as an alternate QB so much as a RB/Wildcat back, and every pass play out of it is kind of like a Ronnie Brown pass: a trick play. Risk didn't pay off this time as he never came close to tucking that ball in, which is why it was fumbled. The risk/reward ratio didn't seem to be worth it in that situation, but hindsight is 20/20 after all.