Can the Counterpoise Correction for Basis Set Superposition Effect Be Justified?

The basis set superposition effect (BSSE) is a simple concept, and its validity is almost universally accepted. So is the counterpoise method to correct for it. The idea is that the basis set is biased toward the dimer because each monomer in the dimer can "use" the basis functions on the other monomer, which it cannot in a simple monomer calculation. This hypothesis can only be tested if basis set free benchmark numbers are available for monomers and dimer. We are testing the hypothesis on a few systems (in this paper Be2) that are small enough that sufficiently accurate benchmark numbers (basis set free, or close to basis set limit; full CI or close to full CI) are available or can be obtained. We find that the answer to the title question is negative: the standard basis sets of quantum chemistry appear to be biased toward the atom in the sense that basis set errors are larger for the dimer than the monomer. Applying the counterpoise correction increases the imbalance by reducing the already smaller basis set error of the monomer even further. Counterpoise corrected bond energies then deviate more from the basis set limit numbers than uncorrected bond energies. These conclusions hold both at the Hartree-Fock level and (much stronger) at the correlated (CCSD(T), full CI) levels. So the answer to the title question is No.