A tweaked ankle, knee or shoulder, a helmet-to-shoulder or helmet-to-helmet hit, etc. are all more likely when a QB is scrambling.
For example, all of Jaren Hall's injury against USU was on a scramble, as was his injury against ASU (his injury against USF was, to be fair, from the pocket).
Taysom's injury against Boise State was on a rushing play, as were his injuries against USU in 2012 and 2014.
I could go on. The bigger hits may come in the pocket, but the injuries seem to come during the scrambles.