Certainly the blood test for ANA (anti nuclear antibodies) indicates all immune deficiency illnesses, including HIV/Aids. However, the same test is for Lupus, Sjorgens (unsure of spelling), MS etc.
I don't know if they have changed the name to CFIDS, I certainly have referred to it as Fibromyalgia, although this kind of only indicates painful muscles and not the multitude of other crap that goes with it .
If, as you say DWP are advising ATOS it is a mental health issue, I wonder if this is why my Medical Report seemed to be based upon depression! I don't have depression, hence why I have lodged a formal complaint to ATOS (still awaiting on this, it's been 7 weeks now.