I don't think anyone has to offer any definitive proof. Even if Google is being a total sweetheart here, it's a conflict of interest and at a minimum, it highlights the importance of strong competition in the search space. The point is to get a scenario where we don't really have to care if Google is inherently biased toward its own products or not.
Companies go about this type of self-promotion in sneaky ways, because they know such tactics won't last long if the first line of code their employees see is `if 'google' in domain: pagerank * 5`. But it'd be naive to pretend like there aren't some people quietly attempting to promote Google's own properties within Google search results, with varying degrees of self-awareness of this fact, from "completely oblivious" (e.g., the search engineer's assumption that a Google-backed property is more likely to be the "correct" search result for a relevant query, and that therefore there is a problem if Google-backed properties are not highly ranked) to "explicitly tasked with finding subtle ways to favor Google's own offerings within the algorithm".
Large companies are necessarily masters of PR/indirection, and they will work to retain plausible deniability, especially after the MS antitrust case.
Companies go about this type of self-promotion in sneaky ways, because they know such tactics won't last long if the first line of code their employees see is `if 'google' in domain: pagerank * 5`. But it'd be naive to pretend like there aren't some people quietly attempting to promote Google's own properties within Google search results, with varying degrees of self-awareness of this fact, from "completely oblivious" (e.g., the search engineer's assumption that a Google-backed property is more likely to be the "correct" search result for a relevant query, and that therefore there is a problem if Google-backed properties are not highly ranked) to "explicitly tasked with finding subtle ways to favor Google's own offerings within the algorithm".
Large companies are necessarily masters of PR/indirection, and they will work to retain plausible deniability, especially after the MS antitrust case.