Correct call. Barrett hit the line before he got knocked backwards. Forward progress, first down.
I agree. He fell back but he had the ball beyond the projected first down line and yard marker just beyond it. When you watch the re-play in slow motion, when Barrett runs into the tight end who is blocking the defensive player, you'll see the stripe of ball appear momentarily so you can tell exactly where the ball is. The tip of the ball is above the yard line. The officials got it right.