This may be somewhat controversial I believe there is a bit of truth in this idea. I’ve had countless sites that ranked for near nothing until I’ve purchased adwords ads.
The rankings are not gifts from Google for buying ads through them, but rather results of manually inspected site relevancy
If you you purchase ads for “blue widgets” then your ad will be “pending review” after the ad. Or keyword is manually reviewed a quality score is given. It is in my opinion that this score is then somehow used in the search algorithm.
Google would be dumb not to use this data, after they have spent time reviewing a website why not use it. A manually reviewed site must be a more accurate measure of a sites “keyword relevancy” than using backlinks and keyword density right?