I don't disagree with your point, but to objectively identify the worries that some people have with Barrett, some other data should be considered.
The passer rating is dependent on reception percentage, yards, and TDs, to be simple. So. . . If one throws short easy passes, that nails number one. If the receiver gets lots of YAC, that gets two, and maybe three. The offense as a whole gets three.
If the worry is that short passes are "easy," and that makes up most of everything else, his rating could be exceedingly high just by, for an extreme example, always passing 0.5 yards behind a wall of three ogre demons. Sure, none of that would say much about him as a quarterback, but his rating would be awesome if they marched downfield for a TD every time.
So, less fancifully, I am curious what his rating is without YAC. A "pure" rating many use. Or even without touchdowns, but rather how far he gets downfield, how often, and how accurately, on any play. This might address things quite differently.