Absolutely false. Google employees have been very clear about this on many, many occasions. There is no relationship
between AdWords advertising and the organic search results. This makes sense, as there would, in fact, be legal issues in many places if they did
allow paid search to influence rankings in the organic results.
Unfortunately, this is another of those urban legends/conspiracy theories of SEO that just refuses to die.
happen is that being visible in both paid and organic search results on the same page can influence the clickthrough rate for both. Sometimes it helps -- people see the listings in both places and are more inclined to click. Sometimes it hurts -- people click on the paid listing (and cost the advertiser money) when they otherwise might have clicked on the organic link and cost the company nothing.
The only way to know if it will help, hurt or neither for your company is to test it and carefully track the results. If you use Google Analytics, you'll especially want to check the Multi-Channel Funnel reports to see how the combination of organic and AdWords is contributing to your conversions.