R3 with one out. Batter strikes out and the pitcher heads for the dugout thinking there are now three outs. The entire defense follows suit and they all start heading for the dugout. R3 and the third base coach are now also convinced there are three outs and they start cutting across the diamond heading for their dugout on the first base side. After crossing the first base foul line R3 is suddenly made aware that there are indeed only two outs. R3 runs over and touches home.
Should the run score or does Rule 8-4-2-p apply to this situation?