I don't have my books available right this moment...
But I believe the FED rule says somehting about "and no other fielder has an opportunity to make a play."
Kind of like the 3rd baseman, playing up, misses a grounder to his left. The ball hits the runner, However the shortstop is behind the runner moving to his right to make a play.... I'm thinking coach is probably correct. Yes, the ball has passed "a" fielder but there is another that can make a play. In his original scenario it was F9.
Somebody needs to look up the FED rule. I'll check back tomorrow.