Quote from Archive.org Page:
Will participation in AdWords or AdSense affect my listing in Google’s free search results?
Google’s advertising programs are independent of our search results. Search results display on the left side of our results page; ads appear on the right and in the colored box at the top.
Participation in an advertising program doesn’t positively or negatively affect inclusion or ranking in the Google search results. Inclusion and ranking are free services; we don’t accept payment to expedite inclusion or improve a site’s ranking for particular keywords. To learn more about how Google ranks pages, please visit http://www.google.com/technology/index.html
So the question of the day is, why was this deleted? I seriously doubt help docs are created or deleted without going through multiple people for approval, including legal. Is Google now, or are they planning to in the future let AdWords and AdSense data influence rankings? Even if they are, I doubt anyone will ever get them to admit it.
Update: Search Engine Land confirms that this removal was accidental and will soon be reversed.