The free-air gravity anomaly and the gravity disturbance are distinct physical quantities in geodesy: the anomaly compares gravity on the geoid to normal gravity on the reference ellipsoid, while the gravity disturbance compares actual gravity on the Earth's surface to normal gravity at the identical point.
The claim states that the free-air gravity anomaly is physically equivalent to the gravity disturbance. In physical geodesy, these are distinct concepts involving different reference surfaces (geoid vs. Earth's surface) and definitions. Paper [4] explicitly defines both terms, showing they are not equivalent. Paper [7] also discusses the definitions and differences in processing gravity anomalies versus gravity disturbances. Therefore, the claim is refuted.