If you do your SEO right and use advertising to build up some brand recognition, you reach the point where your web site appears on the first page of search results alongside your paid ad for your web site.
However, Google has designed their search results to encourage clicking on the ads, so many users who actually find you with search will click the ad you are paying for instead of the search result for your site.
The author presents empirical evidence that not paying for ads doesn't reduce traffic, because users will click the site in the search results, instead of clicking the ad.
That is very much a point, and one that can save people a lot of money if they test it and find their site adn advertising have the same dynamics.