I would not assume that the CBT being proposed for patients with established biomedical diseases is the nice supportive kind. The abusive CBT quacks occasionally publish papers about fatigue or certain other symptoms being a psychosomatic manifestation in these diseases. So those patients are allowed certain "real" symptoms, but an excess of symptoms or their intensity is still psychologized, especially if they persist after any treatment of the biomedical disease (eg, cancer).
How do we tell if the CBT targeting biomedical patients is supportive CBT or abusive CBT? We look at who's involved with it. The two forms of CBT are completely different, despite abusive CBT having hijacked the name of the supportive CBT. The proponents of abusive CBT do not have the training, experience, or desire to use or research supportive CBT. Hence if the usual quacks are involved in CBT for biomedical diseases, it is in the context of abusive CBT, not supportive CBT.