As always, we would have to actually see the play...........Otherwise, we need to go on the information provided by the OP.
Since the OP stated:
"...where he fumbles the ball out onto the field of play...."
It is pretty obvious that the ball is NOT rolling back towards the end zone.
Does K's muff provide the new force to put the ball back into R's end zone? Once again, we go to the OP, which states
"...K1 muffs the ball back into the end zone..."
Once again, pretty obvious what the OP means.
The only question remaining is did R's fumble touch the ground or not? The OP never clarified this point. (rule 2-13-3 already quoted).
Assuming doesn't seem like a good officiating technique to me. If it was, then we might go on to assume that the ballboy tossed a second football onto the field of play during the kick.
