I agree with those drs (who don't belong to the nice/cbt/psych camp) who say exercise is absolutely necessary to recovery. I also agree that exercising in aerobic mode will just add to the existing damage whereas anaerobic exercise is more suitable.
However, that is fine when one has sufficiently recovered and is well enough to do it. If one, say suffers from pots or has palpitations just by standing (as I used to) I can't see how exercise in whatever form is going to help. First you need to sort out such problems then, if the body agrees, start anaerobic exercise.
Regarding the type of exercise, I disagree with the article which advocates low level resistance. High level resistance (weights) and short bursts are what I found most helpful. I have been following the "Body by science" program mentioned on Dr Myhill's website and its been great for my muscle strength but also my aerobic tolerance.