While technically this is correct -- the sponsored and natural results are completely disparate systems -- there are actually some spillover effects we have noticed over the years from adwords advertising.
Namely, a lot of actual search results pages (from search engines and content sites alike) get indexed in Google, along with the adwords-supplied sponsored links.
This results in references to your ad titles, descriptions and display URL within the Google index, and as everyone knows, the more references to your site in the Google index, the better. Even if Google recognizes and takes into lesser account adwords results that it indexes, everything helps.
Case in point: when I search for our company name, which is similar to keywords that are important to our company, literally hundreds of results pages are pages pulled up with our sponsored links on them, which can only help in guiding users to our site.
I expect to hear some disagreement on this, but it is an interesting point in my view that I have not seen brought up before.
Cheers,
mothner