Aside from that person's argument about overhauling the reference systems that we use (surely necessary), that "one-click" priority preference is somewhat problematic. It assumes that all information is equal. It does not take into consideration (or dismisses the notion) that information that has not been digitized or that is behind a pay wall may be better or as important information.
Although the argument makes a claim about 'replicability,' what it really seems to be speaking to is the growing expectation of immediacy --- that is, the apparent moral praiseworthiness we can credit authors or publishers who make it possible to click a link to retrieve a full text document versus the apparent moral blameworthiness of not being able to do so (and instead, e.g., having to find information that is "buried in some library").
Personally, I do look forward to the day when most if not all scientific or scholarly material is freely available as open access, but until that time comes, it seems to me that there would be some serious [moral and practical] implications if researchers intentionally only read and cited literature that is available with a single click of a button and ignored all the rest (as if the tendency to favor reporting positive findings is the only kind of bias that can exist).
Rather, the search and retrieval of good information might best be served by the same kind of activity that P. W. Bridgman described in 1955, that Gerald Holton picked up on in 1994, and that Susan Haack continued in 2003/07 about the scientific method --- that "it is nothing more than doing one's damnedest [...], no holds barred" (Bridgman, p. 534; Holton, p. 78; Haack, p. 24).