HPA axis hypotheses have almost been done to death. The main problem is that basal serum cortisol (or the other markers discussed) is neither a sensitive, nor specific predictor of ME/CFS or symptoms.
Yes there is attenuated morning salivary Cortisol concentrations in some patients but this is not a consistent finding, just like serum cortisol. Note that cortisol is a feed-foward metabolic hormone, as it's main function is to stimulate gluconeogenesis. Salivary cortisol itself isn't terribly important and this can be explained by different sleep-wake activity patterns between patients and controls. There may also be a sort of sampling bias, namely participants who normally sleep in are getting up earlier than normal as they were told to collect samples from certain hours in the morning, for example. (and the participants don't want to admit they're actually sleeping at that time)
Yes, there is no way cortisol is at the root of ME/CFS. Certainly, reduced cortisol might be an effect of ME/CFS, but not the cause. Unless we get into more complicated things like cortisol receptors or something on the cellural level, then there might be something to it.
Also, being sedetary (as is the case in most CFS sufferers) surely affects a ton of hormones, so unless the control group is sedetary as well, finding differences in hormone levels between the two groups is not surprising at all. I am surprised more researchers don't control for this, by including sedetary controls for example. This is quite a great confounder that can't be ignored IMO. What is to say that most positive ME/CFS studies haven't found a result purely due to differences in activity levels? Exercising and being active affects a ton of bodily systems, so finding differences between sedetary and non sedetary individuals is quite likely.