We provide a final state selective experimental study on the direct double photoionization of the valence states of benzene and pyrrole. The experiment is carried out using a magnetic-bottle electron time-of-flight coincidence setup at the incident photon energy region of 25-120 eV. We discuss on the recently discovered phenomenon of so-called Cooper pair formation [R. Wehlitz et al., Phys. Rev. Lett. 109, 193001 (2012)] and show that our experiment provides contradicting evidence on its existence in the proposed form. We confirm the finding of a new two-electron continuum resonance structure observed at about 30–70 eV above the double ionization threshold in benzene, provide further information from it, and suggest an alternative explanation.