I actually think it is the exact opposite. The BPS people love it when patients go on about their illness being physical - this is precisely evidence of the 'unhelpful illness beliefs' that started the whole thing off. If patients take the position that they have no beliefs or opinions about what causes the illness then the BPS theory evaporates on the spot. There is no point in using CBT to change beliefs that aren't there!
Brief statements like "but it's physical" yes.
Due to the effort it takes to think, formulate thoughts and type this is often the only thing patients say, but they could write much about the reasons they settled on this position.
I was "treated" with illness denial early on and it was a disaster. What I and others believed about the illness didn't matter. Manipulating beliefs and nudging the patient towards certain behaviours did not improve symptoms, it merely strained relationships and probably contributed to relapses because it made me persist longer in the actually unhelpful behaviour of trying to force myself to function despite symptoms.
Due to fluctuating severity, I repeatedly ended up in the situation of feeling well enough to try and make the first steps for rebuilding my life. I was enthusiastic and motivated to do it, and did not let fear hold me back. Again, none of these psychological factors really mattered.
The BPSers claim that deconditioning is the cause of many symptoms, and that patients should push themselves more. Yet my experience is exactly the opposite: resting and being easy on myself and asking for support decreases symptoms and helps me get through periods of increased illness severity.
I went to therapy twice and was very willing to try anything and didn't exclude the possibility of some hidden emotional trauma. "Experts" told me this was a thing and I initially saw no reason to disbelieve them. It just didn't work. I've actually tried a lot of embarassing quackery over the years. If I appear close minded, it is due to experience, not prejudice.
I could go on, but it's exhausting. The illness model they propose makes absolutely no sense for patients and that's why we say that it's physical. I don't think they love these kinds of detailed explanations.
PS: I got a bit lost here, the context was actually whether the science points in one way or another. I think it does, but again it needs detailed examination of the evidence and that is even more exhausting. Do pediatricians really think that for example the CPET literature is more consistent with false illness beliefs than some as of yet unexplained organic condition?