Certainly quite feasible to fall asleep at the controls. I once fell asleep at the wheel of my car and subsequently crashed. It was 4.30pm (and I hadn't been in the pub) on a fairly leisurely day (Sunday) with no early start, no work committments. I am at a loss as to how it happened. I was only half a mile from home, so perhaps the prospect of journey's end looming gave me a false sense of security.
I certainly sympathise with someone in the same position, but may be I should have recognised the signs of tiredness approaching more readily.