I sort of assumed we were applying common sense to this equation
so, obviously you admit, then, that overtraining exists. the question now becomes "at what point"?
obviously no one is going to do 20000 reps daily, but "common sense" is perhaps not so common as you may think. i remember posting on t-nation back in the day, when a well-respected poster there named "professor x" was spouting off the whole "no overtraining" nonsense. so some guy comes up and says "i disagree, i was doing x workout". while i forget the exact numbers, "x workout" was something i considered fully reasonable, if high-volume. it was certainly within the realm of many workouts i'd done and seen other do. professor x comes back and says exactly what you just did: "obviously this is stupid and no one would do this workout and i was only talking about volume that sane people would attempt when i said there was no overtraining."

I used to do 9 sets to failure of 15 reps squats twice a week... in addition to many other sets for legs all to failure, and running several miles every day at a high bodyweight. I couldn't handle this. I kept getting more and more fucked up, but I stuck with it because "there's no such thing as overtraining" and "stop being a pussy" constantly echoed through my head, thanks to wise bodybuilders and their wonderful advices.

And this is all besides the point, anyway. The one thing that rarely gets brought up in these discussions is the most important of all... WHAT IS THE DEFINITION OF "OVERTRAINING"? I remember reading some epic, ten+ page article on the subject by lyle mcdonald, and nearly all of it was dedicated simply to the definition of overtraining... and this was in a completely different context than weight training. In fact, the highly detailed definition he was working towards was constructed explicitly in terms of high-volume endurance work, and this is the only type of overtraining definition I've ever seen which has ever been rigorously expounded, hence it's the most commonly referenced... but once again, it has just about NOTHING to do with bodybuilding style exercise. It's laughable when people say "overtraining exists, but bodybuilders don't work hard enough to experience it"... talk about your apples and oranges! This statement is based on a definition of the word "overtraining" that was expressed purely in terms of endurance work... it's not applicable in the slightest!
I would say it's best to use a more general definition of the term when talking about overtraining in a bodybuilding context. The best definition I can think of is this: overtraining is too much training. When is training too much? When NOT doing it would have been more beneficial than doing it.
So, going by this definition, even one bad rep is "overtraining", because it would have been better not to do it. And what usually happens, when one complains of being "overtrained"? Well, at the risk of overreaching, I'd say this: they started off doing good reps, and then got tired, and pushed too far, and started doing reps that damaged their bodies (strained soft tissues, nervous system, whatever, i'm being vague for a reason) such that they could not recover in a reasonable amount of time. Perhaps the person repeats this workout the in the next couple days, or weeks, when, say, their muscles feel recovered (ignoring any nagging pains), and further damages their body, creating a deeper "recovery deficit". Rinse and repeat a few times, and suddenly they go on bodybuilding.com about being "overtrained".
In my opinion, this person has a very good reason for saying so. But some mindless asshole comes along and shouts "NO SUCH THING" because said mindless asshole has instinctively managed to avoid such pitfalls himself. Posting sets and reps is pointless; what matters is whether the damage has been done. There are so many factors affecting this beyond just sets, reps, frequency, that it's laughable to look no further when declaring someone should or should not be "overtrained".
btw, not calling aj a mindless asshole -- he's far from one. just naive, when it comes to this topic.