Tonebender MkIII doesn't sound like it, it IS overdrive...

[Steben]

This "fuzz" always got my dazzled.
looking at the schematic again (as i often do), one could actually see the overdrive thing.

First, you have the darlington pair, which does nothing but boosting. No real distortion there.
BUT ! Much higher input impedance than a normal GE fuzz like the FF or a MkII. About 30 kohms instead of 5 kohms. Which means there is less treble rolloff, even at the guitar's full volume.

Secondly, there is that cap-followed-by-diode/germy trans. AFAIK, this actually leads to a clamping. The cap gets loaded as soon as there is signal. Together with the leakage of Q3 you get a sort of bias of some 100s of millivolts. Ok, no real surprise. However, the couple diode-transistor together work as a sort of clipper. If the transistor would have unity gain (1x) the couple would in fact be a passive back to back clipper. Yet the transitors does boost, giving additional saturation. The onset of clipping, however, is soft. The positive side of the signal gets soft clipped by the diode. The negative side gets soft cut-off (same as in a rangemaster) at the base-emitter transition, a bit as a reversed diode.
In other words, intentionally or not, the diode prevents the hardest saturation possible on a transistor.