Is non-locality stronger in higher dimensions?

A critique of a prescription of non-locality in [Phys. Rev. Lett. 85, 4418 (2000)], [Phys. Rev. Lett. 88, 040404 (2002)], [Phys. Rev. Lett. 92, 130404 (2004)] that appears to be stronger and more general than the Bell-CHSH formulation is presented. It is shown that, contrary to expectations, this prescription fails to correctly identify a large family of maximally non-local Bell states.