The diagnostic criteria probably do matter in the sense that patients who are less impaired are more easily manipulated into reporting improved health.
I am not sure how less impaired is related to diagnostic criteria. A mild or moderate ME patient is less impaired than a severe one, but they are all ME patients.
If you are suggesting less impaired means not having ME, then i can begin to follow, but the answer to patient manipulation is not better diagnostic criteria, the answer is the study is flawed and uninterpretable.