Mindfulness is about creating space between you and your thoughts, not ignoring or discounting them. It allows you to look at them subjectively, rather than being carried away by them. This in no way prohibits you from being introspective, and analyzing the origin of these feelings/thoughts. If anything, it empowers the individual to more rationally grapple with them, without falling into the various psychological traps that often come with certain feelings, such as rumination or avoidance. And whether or not we believe that there is a self, this is no way invalidates the reality that your thoughts ultimately reside inside the mind of a human being, with a real world story. It's unclear to me why the author does not recognize this duality. Most of the literature on mindfulness I've read, including Jon Kabat Zinn's, explicitly mention this duality and its power.