I believe you're thinking of the cable end. Pulling the glovebox only gets you access to the cable side of the rod. The rod goes through the foam seal in the firewall (usually foam is toast) and the other end connects to the door. If there's a problem with the cable, pivot, or rod clip on the pivot, glovebox hole access works. But if the problem is the door itself, you have to take the top off the HVAC housing under the hood.
Pivot lever in pic below. This is the only thing you can actually access through the glovebox hole. The rod just snaps into that little white clip. If that clip breaks...HARD TO FIND. I don't know if they're repro-ing those or not.
Cable hooks to the bottom of that pivot lever. The tip of the lever that holds the blend door in the pic below has broken off.