The impact of cyclic stress was well known from many railroad desasters. The appearance of cracks was quite well known, what was unknown at that times was what we use to call "fracture mechanics" today, the growth mechanism for cracks which may be explosive (instable) under certain conditions. Especially in a thin, highly stressed pressurized skin, the energy released from the skin which is unloaded due to the crack is higher than the energy required to enlarge the crack. It is the same phenomena that makes a balloon go pop if you inflate it high enough (enough energy stored in the rubber skin).

And of course it was the mechanism of coldworking by overstess not understood at that time.

I have heard that when dH reworked the aeroplane to produce the Comet 4 they weren't going to risk another fatigue event so slightly over-engineered the airframe. This made it a bit heavier than it need have been, bad news for any aeroplane. But it made the airframe an ideal choice for Nimrod, which had to operate for long periods in thick air at low level.

Any truth in that?

While metal fatigue was a well known phenomena at the time, I suspect what may not have been so well known was that aluminum has fundamentally different fatigue characteristics relative to iron/steel.
In short, with iron and steel, as long as you have adequate margin between the max stresses and plastic deformation, the fatigue life is nearly infinite, that's not the case with aluminum.

This is not entirely true, there are also iron/steel alloys around that will bite you if you try to prevent fatigue by static margin. Anway this philosophy will lead to structural weight inacceptable for an airframe. An airframe that heavy will have an infinite life because it will not be economic to operate and hence be parked all the time. Except for the military, where cost has not been an issue for some decades.

A Comet 1 with round windows would have had a longer life, but would eventually have failed catastrophically as well. As other airframes did. You can never reliably prevent a crack from happening, whether due to stress concentration, manufacturing flaw, accidental damage or whatever. The trick is to design the airframe in a way that you can allow cracks until you eventually detect and repair them. You need to prevent uncontrolled, instable crack growth. Which can be accomplished by adequate design without the weight penalty of low stress levels. A lesson that took a dozen hull losses and half a century to learn.

Constructing the frames and longerons in such a way, that they divide the skin fields in "fenced-off" sections was the basic method to achieve that.
Previous construction methods had formers attached to the inside longerons or vice versa. That is catastrophic.