I notice that the pilots assert that they were distracted rather than asleep. If they were really asleep, it seems to me that it would be better to admit it than to make up a story about being distracted. Falling asleep is physiologically inevitable if they are excessively tired, whereas not paying attention to their job is a serious and avoidable mistake that can easily justify dismissal. So if they are insisting that they weren't asleep, this fact alone tends to imply that they are telling the truth. Why would they make it worse for themselves?
Of course, falling asleep is a serious problem, too, but, whereas not paying attention is entirely the pilots' fault, fatigue could also be partly the fault of an abusive employer. I suppose pilots technically have the right to cancel their trips if they perceive that they are too tired to fly, but how many pilots actually do that and manage to escape any retribution by their employers?