Myth # 1: Spending money on Google AdWords will influence my website’s ranking in Google's free search results.
Fact: Google AdWords and Google’s free search results are entirely independent of one another. Spending money on AdWords won’t impact your ranking in Google's free search results. Similarly, cancelling your AdWords account won’t lead to your website being banned from Google’s search results
I usually try to explain this as the way the NY Times treats editorial (news) and advertisements - they keep a firewall between the two so they don't influence each other. While that may not be the way some local magazines and free weekly newspapers run (where the biggest advertisers mysteriously often are featured in stories, too) it is the gold standard for ethical publications. I should know, I was on my college newspaper :-)