The metallicities implied by collisionally excited lines (CELs) of heavy elements in H II regions are systematically lower than those implied by recombination lines (RLs) by factors of ~2, introducing uncertainties of the same order in the metallicities inferred for the interstellar medium of any star-forming galaxy. Most explanations of this discrepancy are based on the different sensitivities of CELs and RLs to electron temperature, and invoke either some extra heating mechanism producing temperature fluctuations in the ionized region or the addition of cold gas in metal-rich inclusions or ionized by cosmic rays or X-rays. These explanations will change the temperature structure of the ionized gas from the one predicted by simple photoionization models, and depending on which one is correct, will imply different metallicities for the emitting gas. We select nine H II regions with observed spectra of high quality and show that simple models with metallicities close to the ones implied by oxygen CELs reproduce easily their temperature structure, measured with T e([N II])/T e([O III]), and their oxygen CELs emission. We discuss the strong constraints that this agreement places on the possible explanations of the discrepancy and suggest that the simplest explanation, namely errors in the line recombination coefficients by factors ~2, might be the correct one. In such case, CELs will provide the best estimates of metallicity.