Answer: Jimmy would have done the same as Garrett/coaching staff is doing, no questions asked.
For proof, I'll go to some stats and historical evidence.
First, was Jimmy faced with a similar fumble prone back? By this I mean (gasp!) Emmitt. Emmitt's career attempts per fumble is 72.28. Murray's is 62.33. So Murray is 10-20% more fumble prone. This is a limited data set on Murray, but the numbers are what they are. Nevertheless, this isn't a factor of two we are talking about but doesn't say a lot either way.
Second, was Jimmy faced with a similar decision on benching Emmitt? In 1991, Emmitt fumbled 8 times, all recovered. That is almost unprecedented since its a 50% recovery rate historically. In a 4 game span, he fumbled 6 times (wk 10-13). He wasn't benched, most likely because he didn't lose them so it wasn't as obvious a problem. So that's not the best evidence.
But in 1995 it gets interesting. Mind you we were one of the top teams in the league. In weeks 10-15 Emmitt fumbled 5 times in 6 games. He lost 4 of them. During that stretch the Cowboys were 3-3, with only 1 other loss that season in week 5 (to Washington, HA! In which Emmitt fumbled and lost 1). This year he fumbled 7 times and lost 6, almost an aberration in the other direction. The rest is history, he carried 24 times each in the last two games and heavily in the playoffs. Not sure if Jimmy internally considered benching him, but he didn't do it.
Granted, Emmitt had more "credit" by 1995, but that bad 6 game stretch by the great Emmitt is similar I believe to Murray's bad one currently.