If you cannot work this out with your principal, request a temp 504 Plan to be developed. If that doesn't work, file a complaint.
Most of the time, the alternative activities are identified and completed by a teacher. Developing a 504 Plan will require a different set of individuals.
This was not your responsibility to identify its need. So, they cannot say he has to make up work.
I couldn't have said it any better than you did.
What would be the difference of failing a physically handicapped student with an IEP? This isn't a "for whatever reason" . . . he would be failing the class if he failed to perform the expected activities and could physically do so. The "reason" is exactly what this question is about! This is a temporary situation and the teacher has a duty to find alternative suitable work for his/her student in order that they may have an opportunity to succeed in the class as every other student does, during their temporary hiatus from physical activity.
Here are some things that could hurt your case:
Do you have any information on the grade before the accident? The teacher could say he was receiving a failing grade before the injury.
Did he didn't miss too many days to receive a grade. If he did, the school could make an arguement that is not part of a reasonable accommodation. I wouldn't want to make if it is close, but some schools will.
To me, the school is crazy. I would guess the principal would want this to go away. I just depends on how strongly he or she bows to the PE staff.
Hopefully they understand that if you file an OCR complaint, OCR can, and many times do, expand the scope of their research. If OCR rules in your favor they become concerned that they would treat others just as poorly.