"Why would you have got up at 6am? Surely thats a personal choice which is the cause of you being tired for a legal duty. If you had been called from standby at 6 that would be different obviously."
Most people cannot sleep at will. Circadian rhythms dictate it. This sounds like something that would drivel out the mouth of a company or government hack.
The answer is simple. When you get tired, called fatigued mid-sequence. When that happens a few times, maybe some of the management geniuses will figure it out. But, as long as you accept it, that's exactly what will be shoved up your . . .