The liquid–metal eutectic of gallium and indium (EGaIn) is a useful electrode for making soft electrical contacts to self-assembled monolayers (SAMs). This electrode has, however, one feature whose effect on charge transport has been incompletely understood: a thin (approximately 0.7 nm) film—consisting primarily of Ga2O3—that covers its surface when in contact with air. SAMs that rectify current have been measured using this electrode in AgTS-SAM//Ga2O3/EGaIn (where AgTS = template-stripped Ag surface) junctions. This paper organizes evidence, both published and unpublished, showing that the molecular structure of the SAM (specifically, the presence of an accessible molecular orbital asymmetrically located within the SAM), not the difference between the electrodes or the characteristics of the Ga2O3 film, causes the observed rectification. By examining and ruling out potential mechanisms of rectification that rely either on the Ga2O3 film or on the asymmetry of the electrodes, this paper demonstrates that the structure of the SAM dominates charge transport through AgTS-SAM//Ga2O3/EGaIn junctions, and that the electrical characteristics of the Ga2O3 film have a negligible effect on these measurements.