I would say the only chance at winning something like this is that if he was aimed over the gallery trying to cut a corner and hit someone, then MAYBE would have something to settle out of court. Sort of like hitting a house and liability for damage. Only if the house existed before course was built or the player aimed at, and hit, property on that line off the course would they be liable.
That said, I couldn't imagine what that scene was like and what is in a player's head after that.
That said, the foul ball analogy has some legs, however, some MLB teams have recently put up nets along the field all the way past first and third bases. I bet the reason isn't "exactly" fan protection, per se. My bet is on CYA.