It's not actually that nebulous (I was simplifying because it seemed more appropriate for the setting than to give a thorough discussion of the relevant analysis). The technique, though, is regression analysis, which is widely used in econometrics (amongst other fields) to gauge the marginal effect of various variables. Obviously the exact percentage should be taken with a grain of salt, but those numbers (which are significant at 5% confidence) clearly demonstrate the point.

Again, the Berkman Center's study is very well-done, and if your skepticism remains I encourage you to at least skim it. Otherwise, you're arguing from a position of ignorance and are contributing little to this discussion.