I agree that when running out the clock with under 3 minutes left, or after the 2-minute warning, a pass is needed somewhere, even if the opponent has a TO left.Even Belichick would do that with the Pats. If all you are doing is giving it to your back the other team is not going to shake his hand. They will load the box, get in the backfield, and slam him into the turf. An innocent throw in the flat gives him a break and loosens up the D. Sometimes a short high % pass is like the running game if you stay in bounds.
And it sends a message that the HC trusts the team to pull it off. Much better than running 3 times and giving the ball back.