I think that to a great extent your thoughts are valid, yes. But it isn't quite a simple as it might appear.
The received wisdom is that the adrenals must start to produce some cortisol at about 7 or 8mg in most patients - that is what is described as the physiological dose, what the body produces. However, everyone is different in how their body responds to pred - or the lack of it, so there will be a bit of variation. In addition, cortisol is produced in chunks rather than smoothly trickling into the system - and there will be a bit of variation depending on the time of day you take your pred and the stresses exerted on your body. In my experience, the effect of stress when the body is still sorting itself out is one that doesn't match what you might expect. It seemed to me to happen earlier than you would think and was triggered by a stressful morning trying to deal with call centres and the bank when trying to buy a property!!!!
I don't think the adrenals ever really get into a status where they don't work at all, I think what happens is that the incredibly complex network of hormones and organs (hypothalamus, pituitary, adrenals, thyroid etc) oscilllates in a search for where it is in the right place for everything to work properly. This involves different hormones for men and women - and that partly at least accounts for the great differences we see in how men and women are able to get through PMR and GCA. An endocinologist said much the same.
The slower you reduce at these lower doses, the less dramatic the oscillations are and the less unpleasant patients find it all. But doctors come up with ideas like "the PMR is gone, reduce quickly" - when they CANNOT know it has gone.
In reductions I don't think the mix-up is between PMR flaring and lack of cortisol from the adrenals - the symptoms are different. What is similar is the body's reaction to the pred being taken away - and that isn't quite the same and can happen even at doses well above the physiological dose.
In most people, cortisol is being produced - just not entirely reliably, and it isn't because your adrenals aren't functioning, it is because the whole system is a bit wobbly. In patients where the PMR is actually in remission then the result is struggling to deal with a stressful situation with tearfulness, headache, wobbliness - typical stress reactions. If the PMR is still active you will have a flare of symptoms.
It's horribly complicated, it is something an endocrinologist might be able to clarify - except they don't see the rheumatology side. Anecdotally though, the slower you reduce - and I don't mean only in time but in step size - the less problems crop up.