This sounds like a straightforward denied boarding compensation for the flight on the second day, having absolutely nothing to do with the ordeal the group faced the day before. The only thing where AA did more than the letter of the law is I thought that substitution of a smaller aircraft is one of the exceptions in which IDB compensation is not legally due:
The flight for which the passenger holds confirmed reserved space is unable to accommodate that passenger because of substitution of equipment of lesser capacity when required by operational or safety reasons
(An exception for operational substitution of a smaller plane is BS in my opinion, but that's a separate matter.)