I suffered from severe hyperventilation syndrome and "disordered breathing" about 15 years ago. I'd also gone through a phase of this about 40 years ago, but the first phase disappeared on its own.
I was told that hyperventilating caused the symptoms I had because it reduces carbon dioxide levels in the blood/body. The only symptoms I remember now are the feelings of extreme air hunger and extreme breathlessness, plus lung and rib pain from my desperate (and misguided) attempts to overcome what was happening. I was taught breathing exercises that helped me enormously. I've never managed to eliminate the problem of hyperventilating permanently, but it is something which is now under my control. If the problem restarts I do my breathing exercises again. I wasn't given any psychotherapy, which I think would have been overkill, I was just taught the exercises.
I don't believe from my n=1 experience that ME/CFS and hyperventilation are related, although it wouldn't surprise me if the symptoms that arise from hyperventilating were mistaken for ME/CFS by doctors who didn't know anything about ME/CFS or disordered breathing. But I don't believe that people with ME/CFS are completely exempt from developing hyperventilation syndrome either. Personally, I think the conditions are independent of each other, and people could end up with one or the other or both or neither. But unlike ME/CFS hyperventilation syndrome can be helped with the right training. (It took about 20 - 30 minutes for my first "lesson" then a follow up of less than 10 minutes. I was then capable of dealing with it myself whenever the need arises.)