This study concerns the way to describe some physical properties of simple liquids by using the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. It constructively analyzes the recent contribution of Sarkisov [G. N. Sarkisov, J. Chem. Phys. 119, 373 (2003)] on the structural behavior of a simple fluid near the liquid-vapor critical point. His work, already compared with computer simulation studies, is here brought into direct contact for the heavier condensed rare gases Ar, Kr, and Xe with (a) experiment and (b) earlier theoretical investigations. Directions for future studies then emerge. (C) 2004 American Institute of Physics.