FWIW, one of my sites always ranked in the top five for the first word of it's two word "brand" name. It's not a keyword anyone is trying to rank for, it's just part of the brand name. As an example, let's call it Swift Widgets and as an example say it's ranking for the word "Swift." The site itself was never about "Swift" (example). "Swift" is just a descriptive word that made the domain a brand name. The single word never delivered traffic because nobody searches that phrase.
Nevertheless I think it is an interesting measure of how much incidental weight was being placed on the word in the domain (particularly via anchor text) to rank it, versus how much the site is actually about that word (which is zero, it's not about that word).
The site has been ranking in the top five for a few years but this year started to slip and most recently has dipped to the second page of the results, which is pretty much where it belongs, if at all. So from this one example, it could be said there is evidence that Google may be dialing down some of the noise from incdental anchor text influence.