I didn't give a definition of overtraining. Overtraining would be training more than one's physiological capacity could keep up with. That is, training too often before the body is able to supercompensate, and reaching a stage beyond the alarm and resistance phase (exhaustion) of the GAS which could cause a regression of that which was gained.
One could potentially overreach over several weeks (thus generating very high demands on the body as a system) and garner huge gains (this technique was developed by Brian D. Johnson and assigned the term "blitz"). To continue doing it for a long period of time, beyond that which should be tolerated, would classify as overtraining, and eliminate all of the positive affects of the blitz. Once you reach a point (in accordance with the GAS) of exhaustion, you'll probably lose everything worked for (or at least cease progress which could remain for a while).
I would argue that any intermediate or beginner who doesn't progress in some way in every workout is either undertrained or overtrained. People tend to do things in excess.
Mike Mentzer HIT is probably the most obvious example, with Arnold's ultra HVT being the other. They either excessively overtrain or excessively undertrain. My observation typically suggests that intermediates who workout with high or moderate intensity and carefully adjust their frequency and volume to correlate with it (viz. moderate intensity, 3-4 sets per exercise, 5-7 exercises, 3-4 times a week / high intensity, 1-2 sets per exercises, 5-7 exercises, 2-3 times a week), depending on their genetics, make the fastest progress during this phase.
Guys like Mudge, LAM, Gopro, etc. (who are, as illustrations, very advanced) will have to be more careful in finding out what is affective for themselves as individuals. Once you near your genetic capacity, things get much more difficult..
That's when these "one-size-fits-all" programs become completely inapplicable, mainly because we all ARE individuals and must evaluate the measurements to correspond to our own physiology. Optimizing this process is probably the hardest thing a trainee will ever have to do, and if you employ a run of the mill personal trainer to help, you'll probably be lost within the span of a few weeks. My advice? Hire P-Funk...