The electronic structure of the double octahedral layers present in H0.33MoO3 has been studied. It is shown that, depending on structural details, three bands, two of them having a two-dimensional character and one having a one-dimensional character, can be in competition at the bottom of the t(2g)-block bandstructure. Both qualitative arguments and detailed computations show that the Fermi surface of the double octahedral layers has a two-dimensional character and does not exhibit nesting vectors. Consequently, the metal-to-insulator transition exhibited by H0.33MoO3 cannot be a Fermi surface driven electronic instability, as recently proposed. An order-disorder transition of the protons is suggested as a more likely origin of this resistivity anomaly.