It's not so much about the narrow targeting as it is about the engagement. These "advertisements" show up in your FB news feeds and Pinterest pages because someone else in your community thought it worthy to share; they go viral when many people find it worthy to share. They're also much more integrated to the platforms as they don't initially appear as advertisements, unlike say banner ads.

"I still have such a hard time believing that they actually convert into user action (eg. purchase)."

To your last point, the author argues that native advertising is more akin to Brand advertising versus direct response, so in the same way, they're not intended to function as direct response ads that encourage you to buy immediately. But I'd argue that these native ads are even more effective because they can serve both purposes; they can serve the purpose of bringing brand awareness as merely being subtly place subject matter into and article that brings awareness to a brand, or they can be as direct as a product endorsement by a celebrity on their Twitter feeds or Pinterest pages. Native advertising can be versatile enough to cover both direct response and brand building advertisements.