I agree it should say "kick" crosses ..., but would that mean the related kick or any kick during the down? The related kick is not something I'd thought about until today!!
In the brain teaser, I don;t agree that the ball crosses the NZ, we don't have a definition of ball crossing the NZ, though the two definitions that concern the ball crossing the NZ that we do have (pass and kick) both refer to the ball touching something beyond the NZ, so by extension I believe that the ball crossing the NZ would use that criteria as well.
However, how about this:
4/10 @ A-20. Team A punts and kick is blocked at A-10. While ball is loose behind NZ B20 blocks in the back at A-15. A1 recovers at A-5 and runs to the A-25 where he fumbles. B2 recovers at the A-30 while grounded.