If it was a training exercise, surely the trainer would have intervened long before the stall.
TUC at 28,000 ft is 2.5 to 3 minutes… given some people can march up Everest without oxygen, that 3 minute number is probably (rightfully) on the conservative side.
I would assume the 695 has a cabin altitude alert together with a chime should the cabin altitude exceed something like 10,000 which makes it hard to believe the crew failed to recognize a surreptitious depressurisation.
Not a lot makes sense with this incident. Structural failure? But in all likelihood it was smooth air up at FL280, so that rules it out.