This is far simpler than the author makes it out to be. "Authentic" means you believe in it. "Inauthentic" means you think I believe in it, and you're condescendingly pandering to my tastes to make a buck. From the article:
Authentic: You believe in your $5 pour-over.
Inauthentic: You believe I'll buy a $5 pour-over because you don't respect me.
Authentic: You, the coffee shop I've never heard of before in 1989, using "Tall" "Grande" and "Venti" because... something.
Inauthentic: You, the coffee shop I can't get away from in 2016, using "Tall" "Grande" and "Venti" because they're your brand.
Authentic: underwear branded as some name that has value only for the name.
Inauthentic: underwear branded as some name that does not have value in its name.
(an "inauthentic" pair of boxer shorts would say, for example, DKNY. And yes, I know they make boxer shorts. But having 'DKNY' on a pair of boxer shorts doesn't have the same weight as Marks & Spencer, at least not for people who shop at Marks & Spencer)
It gets even simpler:
Authentic: Based on a true story.
Inauthentic: Pretending to be based on a true story.