Finally, any player may bat a fumble or pass in flight, including batting it TO a teammate. So this is not the only legal batting.
Maybe I am reading this incorrectly, but here is an illegal batting situation
A is in punt formation and the ball is snapped to A1, who turns his back to the line of scrimmage and throws a backward pass into the air. A2 comes forward and bats the ball 20 yards downfield where:
(a) A3 recovers it 5 yards beyond the line to gain; or
(b) it is caught by A4 who advances for an additional 5 yards; or
(c) it goes out of bounds in advance of the line to gain; or
(d) B1 intercepts and returns it for an apparent touchdown.
RULING: In (a), (b), (c) and (d), the batting by A2 is illegal. In (a), (b) and (c), it will be B's advantage to accept the penalty of 15 yards which will be administered from the spot of the foul because the batting occurred during the loose-ball play and behind the basic spot. In (d), because the foul was during a loose-ball play, before a change of possession, B may keep the touchdown by declining the penalty for A's foul. Otherwise, the penalty will be enforced from the spot of the foul and A will retain possession of the ball if B accepts the penalty. (10-5-3)