A good way to determine if a new force has been applied to a grounded ball is answer three questions:
#1. Did the applied impetus change the forward/backward direction of the ball? In other words, did it cause a forward-rolling ball to go backward? Or vise-versa. if it did, it's a new force.
#2. Did the applied impetus cause a stationary ball to start moving again? If it did, it's a new force.
#3. Did the player applying the applied impetus do so intentionally? If so, it's illegal batting/kicking.
In the case of the errant snap, the initial force is the snap, and as long as there was no intentional effort by either team to put the ball in the endzone, they can bat it around all they want, as long as they don't change the initial direction, it's the force of the snap that puts the ball in the endzone. So, safety.