We use the standard fermionic and boson-fermion Hamiltonians to study the BCS–BEC crossover near the 202 G resonance in a two-component mixture of fermionic atoms employed in the experiment of Regal [Phys. Rev. Lett. 92, 040403 (2004)]. Our mean-field analysis of many-body equilibrium quantities shows virtually no differences between the predictions of the two approaches, provided they are both implemented in a manner that properly includes the effect of the highest excited bound state of the background scattering potential, rather than just the magnetic-field dependence of the scattering length. Consequently, we rule out the macroscopic occupation of the molecular field as a mechanism behind the fermionic pair condensation and show that the BCS-BEC crossover in ultracold gases can be analyzed and understood on the same basis as in the conventional systems of solid state physics.