For me, the issue isn't authenticity, it's
artifice.
I like old-school play with a hard landscape milieu and a principled, neutral referee, because those are the conditions that minimize artifice. The game-world is what it is, what happens happens, decisions have consequences, and all victories and defeats are honestly earned. You may not get satisfying narratives or character arcs out of the deal, but at least you know the referee isn't putting a thumb on the scale to hand the players unearned wins.
Both trad and post-trad, on the other hand, traffic in artifice. In trad games, the mechanics don't really support narrative, so it's expected that the GM will fudge and rubber-band and palette-shift and resort to whatever other soft railroading techniques are required to force desirable outcomes without the players being too overly aware of the GM's invisible hand at work — or at least, without giving the players an excuse to drop the polite fiction that the game isn't being quietly directed.
Post-trad games are considerably more honest, in that they foreground the very mechanics that guarantee a story will happen, but in doing so they also foreground how artificial the whole process is. If old-school is an honest game of poker, and trad drifts between being delighted by an entertaining stage-magician and playing blackjack with a crooked dealer (one with a grudge against the house who occasionally slips you a face card from the bottom of the deck), storygames are watching a
Penn & Teller routine where they show you how the trick is done.