ME is definitely a biopsychosocial illness. This isn't the same as thinking that psychological therapies can make us better.
I'd agree if we stick to Engel's original intentions with the term biopsychosocial. Unfortunately that's not how the term is used now.
Therefore, in today's terminology I'd say ME is a biological illness.
I think the origin of the concept with Engel in about 1970 is fascinating - the example he gives is of a hypothetical man having a heart attack (biological factor). His interpretation of the chest pain (psychological factor) affects how quickly he goes for help, and the response of the hospital staff, eg a mistake or delay (social factor), effects the outcome. Thus it is not his belief in itself that alters the outcome, but the way it influences how quickly he goes for help.
In that sense, his heart attack and every other illness is biopsychosocial. Engel's aim was to highlight that doctors should not just look for biological factors such as blood pressure and blood tests, but should look at psychosocial factors which may alter his chances of recovery, eg will a patient take the pills he is prescribed, does he live in a freezing house, does he eat a healthy diet etc.
The BPS clowns we know and love (!) have taken this to the extreme of forgetting the biological altogether, or paying lip service to it while ignoring the evidence that, for example aerobic exercise is detrimental.
They have made up a theory that it is a psychosocial illness caused by a (hysterical) fear of exercise and false illness beliefs which can be cured by persuading patients they have no biological illness and getting them to exercise. They try to give it legitimacy by using fancy terms including somatisation, conversion disorder and the biopsychosocial model. This made up theory has no proof, and all the research both biological and clinical trials of CBT and GET prove it wrong.
So although, in Engel's terms ME, like all illnesses, is biopsychosocial, that is different from the now more common use of the term biopsychosocial for illnesses that doctors and insurance companies and government benefits departments decide aren't real and blame the patient if they don't get better.
On those grounds, I refuse to call ME a biopsychosocial illness.
The modern version of the biopsychosocial model is a belief system about unexplained chronic symptoms, which is unproven, unprovable, and wholly detrimental to patients, leading to prescription of unproven psychological therapies instead of proper medical investigation.