Here's what I'm guessing happened:
(1) Group didn't have seat assignments
(2) Flight was overbooked
(3) No one volunteered to take a VDB
(4) IDB rules hit the non-status passengers with no seat assignments first
(5) The school group refused to split up. I can't imagine that there wasn't a second adult who could have accompanied the second group of students.
(5) AA decided to hold down the letter of the rule and treat the decision not to split as a voluntary no show and canceled the tickets.
(6) The school leader went ape and all attempts at a reasonable solution (e.g., getting to DC before Wednesday which would be super easy - there is definitely space via connecting cities, etc.) thus became unsuccessful.
Honestly, if it went down as above - and assuming there was a second adult - I'll side with AA.