You forgot to mention that while Geno threw a high amount of screens, many of those attempts equal negative yardage, so they bring down his average considerably. He actually threw WAY LESS passes in the 1-5 range than any of the other QBs.
Barkley actually threw the most passes (in terms of percentage of attempts) less than 5 yards by quite a wide margin. And on top of that, his accuracy in the 1-5 range was WAY below average.
This actually has been discussed before and the bottom line was that it benefits Glennon most.