It's been established (with evidence) that the goal line is the black line in FRONT of the white line. If the ball hit the white line when it came down (as the photographic evidence shows), then it's a goal. If the AR believes, during the game of play, that it is NOT a goal, then he should have done as you said. The AR didn't. Instead, he ran back to midfield as ARs do when a goal is scored. At the end of the day, you can't argue the facts and the evidence with opinion. If you want to really just blame someone, blame whoever left the player open to take that shot
Nobody is disputing the fact that the black line is the goal line. However, the ball can hit the white and still not be a goal. The entire ball must cross the black. Just because a portion of the ball hits white does not mean the entire ball entered the white area.
Also, you are completely wrong about the AR responsibility. On a straightforward goal, yes tha AR turns and runs toward the center line, no flag. On a questionable goal with play continuing, if the AR believes it to be a goal, the AR should stand his ground, raise his flag, make eye contact with the center and then run toward the center line with his flag still raised.
