Welcome, Delta51, to our forum. May you find it both enjoyable and informative. Let's make it 2nd & goal from B's 3, for an easier explanation. The end of the run would be the basic spot, and A's fumble was the force that placed the ball in the EZ = touchback if ball is then muffed OOB in there. The illegal bat would be enforced from the end of the run w/2nd & goal @1. IF the fumble had occurred in or behind the LOS, with the same results, it would now be treated as a loose ball play (10-3-1c) with previous spot enforcement.
Your possible answer to some of your local officials : " Geez, guys, the fumble occurred at the line of scrimmage and under ole' 10-3-1c, would be classified as a loose ball play with previous spot enforcement
. Guess you guys pick up my post meeting treats tonight
."
NOTE : In the OP, with the end of the run and the LOS the same, the same results would occur but hopefully your buddies will be impressed with your research.