I don't think the school is liable. If your son had slipped on an icy curb(like another poster did), then their insurance would pay(like homeowner's insurance would) If you didn't even think that the finger was broken when he got home, they couldn't know hours before that, IMHO. If it hurt that much, he should have asked to call you. They probably assumed it had just been bent back by the football(overextended?) If he had continued to complain, they would have sent him to the nurse. Did he keep playing once the finger was hurt?
Was your son playing football? I really don't know how he could know it was intentional. If it had hit him in the back, that would be another story. Was his hand up to catch the ball or what? I don't know how you would prove intent on that. The other kid was rude to laugh, but maybe he didn't realize your DS was really hurt(noone else did, even you, right) Kids are like that, especially at 9 or 10. Besides, there are two sides to every story, and usually the truth is somewhere in between(speaking as a teacher and a parent here)
When DS was 8 or 9, he got his cornea torn at school. A little girl stuck her finger in his eye, admittedly on purpose. It was not just scratched, but torn and the ER thought they may have to actually suture it

They gave us some ointment and a patch, and luckily it healed enough by the following afternoon, so that he didn't need anything except the ointment and patch for a few days. I too thought the school would pay for what insurance didn't. They said they don't cover things like that, but that I could go after the family for the OOP charges and my 1/2 day off work to take him to the Opthamologist. I decided that would be too much drama. My DS and this little girl had been doing the love/hate thing for months and I am sure he did something to her at some point. She didn't have any idea poking someone in the eye could do more than make someone cry, I am sure. Besides, you don't know how someone else's parents may react. Maybe this child is beaten at home and this could cause a really bad scene.
Marsha