Entangled two-photon absorption (ETPA) has recently become a topic of lively debate, mainly due to the apparent inconsistencies in the experimentally reported ETPA cross sections of organic molecules obtained by a number of groups. In this work, we provide a thorough experimental study of ETPA in the organic molecules Rhodamine B (RhB) and zinc tetraphenylporphirin (ZnTPP). Our contribution is 3-fold: first, we reproduce previous results from other groups; second, we on the one hand determine the effects of different temporal correlations─introduced as a controllable temporal delay between the signal and idler photons to be absorbed─on the strength of the ETPA signal, and on the other hand, we introduce two concurrent and equivalent detection systems with and without the sample in place as a useful experimental check; third, we introduce, and apply to our data, a novel method to quantify the ETPA rate based on taking into account the full photon-pair behavior rather than focusing on singles or coincidence counts independently. Through this experimental setup we find that, surprisingly, the purported ETPA signal is not suppressed for a temporal delay much greater than the characteristic photon-pair temporal correlation time. While our results reproduce the previous findings from other authors, our full analysis indicates that the signal observed is not actually due to ETPA but simply to linear losses. Interestingly, for higher RhB concentrations, we find a two-photon signal that, contrary to expectations, likewise does not correspond to ETPA.