I think the problem comes in in that fans of Garrett believe a big part of the reason he was freed up from play calling duties was that the owner wanted him to concentrate on other aspects of managing the team overall and on organizing the defense in particular. People who don't like Jason Garrett prefer to see it as a 'demotion' and simply removing the head coach further from the equation. So, again, it comes down to guessing about what we don't know first-hand.
That said, the defense improved a lot more than the offense did this season on a relative basis, so the change wasn't all play calling. Given how many positive things the players, staff, and front office say about Jason's involvement overall, I think you'd have to be willfully naive to think that the guy was relieved of play calling responsibilities and didn't put that time to good use elsewhere this season. Running an NFL team has got to be incredibly demanding work in terms of managing details. It's not exactly a stretch to think that he was probably over-tasked with the play calling included, but that it wasn't until this year that he had somebody on the offensive staff who'd run a game the way he'd want it run and where he was comfortable handing over the load. I have zero problem with the idea that Linehan may just be better at the gig than Jason will ever be. That's what you want: the best guy for the job doing the role he's best at doing.
But this notion that Jason is just a walk around coach in charge of clapping is a juvenile fantasy ginned up by people who just won't recognize that the HC is doing a good job. There's *no* way you earn the professional regard Jason has earned in Dallas all the way around without delivering real value. We've all seen what happens to coaches in this league who don't have the respect of their staff, their players, or their GMs. Without exception, they fail.