Yes, I am mixing metaphors a bit here. In Google's case, however, they are not simply presenting hyperlinks. They are prioritizing which links appear on top and those that appear on page 2. So they are having some input as to how those links are presented. One wonders what links are being ignored or tossed aside in order to present the results. Here's an example. I Googled Jan 6 Capitol Riot. 6 pages in I do not see a single link referencing any Fox News regarding the riots. If Google is curating what gets presented in a search result then I'd say they are "publishing" the results. If it's a random, alphabetized list, then fine.
As for accuracy of information, I was really thinking more of FB because they do take a direct hand in determining what is "factual" and what isn't. The overall point, if you "publish" or editorialize posts then I think you bear some responsibility for that.