This is all rather fuzzy - perhaps deliberately so. Because the Chalder formulation does assume that patients have abnormal illness beliefs & behaviours I read it as actually proscribing that model and only allowing CBT formulations based on coming to terms with living with a chronic illness - as is sometimes offered to patients with other serious long-term conditions.
They're pretty much doing a "foot in the door" thing where CBT is mentioned as an adjunct support treatment for the few who could have some minor benefit from it, then going with the idea that their CBT is based on this fear model, thus their fear model of CBT is recommended, even though the guideline doesn't actually recommend it, it pretty much just says it exists, is available and commonly used. Despite actual evidence of efficacy.
Which is a fundamental problem with the CBT format, it's anything anyone wants it to be, and anyone doing a CBT course will customize it to their liking, so none are ever alike. In systematic reviews everything it contains is compressed down to the single initialism and concept of CBT. It could be CBT that teaches about astrological projection and it would literally make no difference, it would still be CBT because CBT is a process. It could even teach antivaccine conspiracy fantasies and it would still fall in the same category as any of the psychosomatic models. Hell, it could even teach helpful things that are the opposite of Chalder's model and it would still be in the same category in a systematic review.
What's even more absurd is that from the study it doesn't seem that any of the participants even partially recovered on the terms they describe. I didn't bother too much but nothing indicates that. And yet they actually present it as a success, a reader would have to go through a, frankly, unnecessary long and meandering paper to know it. But most will simply read the abstract and quickly scan down, and go with the propaganda they put as a conclusion.
This is propaganda on the same level as what the tobacco industry did.