WOW Kirby! What timing...(are you in Michigan?)
I'm having the same BIG issue with what appears to be a conflict between the Rule and Case Books - assuming the penalty is declined (which is pretty remote). But I agree that it should be A's choice.
Some other interesting issues/questions:
1. Since this is an illegal kick, treated as a fumble, was team possesion ever really lost? For that matter who actually was the last PLAYER in possession DURING this down. Since a down starts on a snap, and the kicker never "possessed" the snap, it seems nobody was; but a fumble remains in possession of the fumbling team until there is a COP or the play is blown dead.
2. Now, if team possession WAS lost, where was it lost? At the snap; where it was muffed; where it was illegally kicked; or when the loose ball was blown dead? This would have an impact on from where the down would be replayed.
3. If there had been no IW on this play, could A have advanced the illegal kick/fumble? (I'll bet somebody would be blowing a whistle if A did; and would that be an IW?). If they reached the line to gain, could it be a first down?
4. What if this were the last play 1) of the second quarter; or 2) of the game? Since an accepted penalty would result in a safety, the second period would not be extended; but at the end of the game, it could be.
Again, if this is only an error in the Case Book (and the play has been there since at least 2007), there still, at least, is a question regarding from where the ball would next be snapped if the penalty was declined.