Massive early-type galaxies (ETGs) show several strong CO absorption features in their H- and K-band spectra that cannot be explained by state-of-the-art stellar population models. For many years, the disagreement has been attributed to the presence of intermediate-age stellar components that are dominated by stars in the asymptotic giant branch phase. However, no robust evidence of this scenario has been provided so far. One way to test this claim is by comparison of CO indices for ETGs and for relic galaxies. Lacking the intermediate-age stellar populations, relic galaxies provide us with a unique opportunity to address the origin of strong CO absorptions in ETGs. Here, we utilize the prototype relic galaxy NGC 1277 and compare the CO absorption features of this galaxy with the ones of a representative sample of massive ETGs. We show that the CO lines in both systems have similar strengths, significantly stronger than the predictions of stellar population synthesis models. We conclude that intermediate-age stellar populations in massive ETGs are not the culprit of the strong CO absorptions.