I don't claim to know the details, and I look forward to Moro's group publishing a lot more work on RECAF so it can be subjected to critical review by scientists and all the rest of us.
However, there is the following possibility. CA-125 may be 'ineffective' (i.e., non-specific) at detecting ovarian cancer not because it fails to detect the cancer per se, but because it detects (i.e., gets confused by) other factors (e.g., spurious proteins) that are present in the tissue samples. If RECAF does not react to these spurious factors then it could effectively help eliminate them from the combined test, resulting in a more specific test for ovarian cancer.
I don't know if this is the actual scenario with CA-125, but it is within the realm of possibility. RECAF may be helping not by increasing true positives, but by reducing false positives.
QB