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:

Shaken caffeine-guzzlers told the Guardian that they felt “duped” and “upset” because they’d thought it was an “independent” coffee shop. A rival coffee hawker sneered that Tesco was “trying to make money” out of “artisan values” – although, presumably, so was he.

Authentic: You believe in your $5 pour-over.

Inauthentic: You believe I'll buy a $5 pour-over because you don't respect me.

Today’s heroically “independent” baristas are profiting from a market that, in the UK, wouldn’t exist without the trail blazed in the 1990s by the now-despised big chains, such as Starbucks.

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.

Even Marks & Spencer’s men’s underwear is branded “authentic”, posing the nice question of what an inauthentic pair of boxer shorts or trunks would look like.

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:

When it turned out that James Frey’s “memoir” A Million Little Pieces was fictionalised, the author was pilloried for having exploited so deftly the way we venerate real emotion and experience.

Authentic: Based on a true story.

Inauthentic: Pretending to be based on a true story.

This is one of my favorite Hubski conversations of all time.