Anyone who thinks that being physically knackered (i.e. unable to pedal up anymore hills) doesn't equates to incompetence to drive a car (It still requires concentration!) is beyond reasoning with. Driving tired is compared to driving drunk and is thought to be a widespread but underreported contributory factor in crashes. There's a summary at http://www.roadsafetyobservatory.com/Review/10061
A quick read shows that their use of the term fatigue is about fatigue from driving, ie tiredness bought about by long term driving and the monotony of that task. It is an entirely different thing to physical fatigue through exercise.
Exercise is a commonly used relief from that type of fatigue.