Well as with most things related to human behavior, explicit quantitative proof is a rarity so we rely on other measures including observation, survey, interview, and other tangential data to formulate a supported conclusion albeit usually somewhat speculative. However, there is explicit proof that hormones (including testosterone) is present in saliva... Salivary Testosterone Measurement by Liquid Chromatography Tandem Mass Spectrometry in Adult Males and Females. Additionally, "Studies have shown that the mucosa membrane inside the mouth is permeable to hormones such as testosterone that are found in saliva (Dobs, Matsumoto, Wang, and Kipnes, 2004)" (disclosure; I did not look up that referenced study). During "Romantic" kissing or open mouth kissing by nature saliva is obviously intermixed or better known in common vernacular as "swapped".
In regards to the last link (Sex Differences in Romantic Kissing Among College Students: An Evolutionary Perspective), yes the authors state in the introduction where they are laying out their hypothesis, that the statement is "speculative", however in the discussion section they argue the results of their various studies along with findings from other scholarly studies support the hypothesis they laid out in the introduction. And as is commonly found in behavioral analysis, they acknowledge the limitations and call for further study but their final statement includes... "Nonetheless, this study provides evidence that romantic kissing may have evolved as an adaptive courtship strategy that functions as a mate-assessment technique, a means of initiating sexual arousal and receptivity, and a way of maintaining a bonded relationship."
The last article I'll refer readers to is Saliva: Secret Ingredient in the Best Kisses (Media bias/fact check report for the source publication... https://mediabiasfactcheck.com/live-science/)
And my absolute last word on this subject... Kody's direct quote was “When you kiss the person that you kiss, the hormones go into your mouth and it registers certain things that will stimulate both the heart and the body for other reasons, ” While very clumsy and awkward, hormones do indeed go into your mouth and kissing does stimulate both the heart and body so yeah, he "wasn't that far off the mark" as @Gothish520 put it.