A true statement, as far as it goes. In general, the more in-links you have the higher you'll be ranked in the search results. But as we've seen, links confer different amounts of importance, and a high quality link can easily outweigh several low quality links. You will get better results in the search engines if you have link popularity from sites that have considerable traffic . The statement starts off dead on, then misses the point completely.
Traffic has nothing to do with link popularity.
Traffic contributes nothing. Although all incoming links improve your importance, the FFAs, whose lots of out-links dilute whatever importance they might have, will contribute very little. The .gov or .edu by themselves confer no additional authority, but these sites might be more likely than your cousin's to have lots of in-links themselves, and so have a high PageRank. The main lesson here seems to be the same old one. Easy to navigate pages with high quality content will attract links from Webmasters augmenting their sites by linking to yours, and it is those incoming links, hopefully from sites that are themselves important, that will boost your page's importance.