Shape coexistence in the nuclei (182-192)Pb is analyzed with the Hartree-Fock-Bogoliubov approach and the Gogny force. Good agreement with the experimental energies is found for the coexisting spherical, oblate, and prolate states. Contrary to the established interpretation, it is found that the low-lying prolate and oblate 0+ states are predominantly characterized by neutron correlations whereas the protons behave, in general, rather as spectators than playing an active role.