It is common knowledge among experienced AdWords advertisers to see an organic ranking increase as a result of an extended AdWords campaign. However, you are correct to point out that correlation does not imply causation.
From my experience, any type of significant promotional activity, applied to useful content, will indirectly influence natural ranking signals. It is important to understand that it is an indirect effect, though an effect, none the less. You will see the same type of effect from radio, TV, and print advertising campaigns. It isn’t favoritism from Google, it is the natural result of promoting your website content.