There is still a significant stigma associated with mental illness, both in the medical profession and in the general public, which often view mental illness or psychological factors as less serious or less real than physical disease or organic factors. ME/CFS patients were regular people once, ME/CFS does not make people immune to harbouring the prejudice and misconception that we can expect to find in a general population sample. Additionally, after being treated like garbage due to their alleged mental health status or psychological factors in physical illness, it would be unsurprising if some ME/CFS patients started to think the same.
That said, I agree that the psychiatric stigma as an explanation for ME/CFS patients' resistance to biopsychosocial explanations/treatments, is massively exaggerated. It amounts to little more than a strawman and red herring to distract away from addressing criticism. The possibility that some patients may want to avoid the stigma of mental illness is massively overshadowed by the real issues at hand. Patients want an accurate diagnosis with adequate descriptive and explanatory power, want the correct treatment, do not accept the stigma of labels which do not apply to them, do not want limited research resources to be wasted on blind alleys and psychobabble, are concerned about the negative implications of ideology and inappropriate treatments, and can analyze the claims for themselves and spot flaws.
Some patients have suggested that the stigma surrounding ME/CFS is comparable to or even worse than the stigma surrounding mental illness. For example, major depression may not get much respect, but it is still generally acknowledged and treated; whereas ME/CFS is often dismissed entirely and even openly ridiculed in front of the patient without any treatment. I have even come across one or two anecdotes of people applying for disability benefits based more on their secondary depression rather than their primary ME/CFS.
Consider the following thought experiment. Suppose you are at a gathering of about 1000 people including hospital staff, politicians, and their family and friends. For whatever reason you are on stage with the microphone and have to introduce yourself as a patient. Which would feel more cringe-worthy: "I have severe major depressive disorder", or, "I have severe myalgic encephalomyelitis and/or chronic fatigue syndrome". I do not expect everyone to say ME/CFS would be worse, but I think enough would say it or have trouble choosing, demonstrating that ME/CFS is not a shield to stigma.
Patients allegedly seek a medical physical sounding diagnosis to avoid facing up to their psychological problems, to avoid the stigma of mental illness, and for secondary gain. As it has never been demonstrated that ME/CFS patients have primary psychological problems, nor question the CBT/GET model primarily due to secondary gain or fearing the stigma of mental illness, we are left with patients wanting a medical physical sounding diagnosis simply because it matches the characteristics of their illness. I'm just preaching to the choir here, but I imagine this thread would not go down well at the next conference on psychosomatic medicine where such criticism would not be welcome.
Wessely et al have speculated about medical labels helping patients to avoid stigma, blame, guilt and responsibility. At first it was aimed at patients more in general but now the target is critics of the biopsychosocial approach to ME/CFS. Ironically, Wessely et al have totally avoided blame and responsibility for any negative impact of their approach. Even though they have occasionally conceded (but still downplayed the impact) that some doctors contribute to the stigma of mental illness, all roads more or less lead back to primarily blaming the ME/CFS patient.