So devastating could Rich's hatchet jobs be that he was known as "The Butcher of Broadway".
In a gripping barroom showdown on the eve of opening night, Tabitha bluntly admits she's already sharpening her knives: "I'm going to destroy your play," she informs Michael Keaton's Riggan Thomson, whose fortunes have been made, and credibility marred, by his lead role in three blockbuster films about a superhero known as Birdman.
To her mind, Thomson is clogging up the theatre district with a show which, for all its artsy trappings (it's an adaptation of a Raymond Carver short story), is just a vanity project. Wounded in some primal way, as if given a violent sexual brush-off, Riggan retorts that her criticism is worthless, thereby apparently sealing his fate.
Some have suggested that this encounter is one of the few jarring scenes in Alejandro Gonzalez Inarritu's Oscar contender.
"Someone could have told Inarritu that critics, though often mean, are not pre-emptively so," complained Anthony Lane in the New Yorker.
But although Tabitha may be unusual in voicing her opinions direct to the soon-to-be-injured party, those views clearly represent staunch convictions against celebrity-powered productions.
I'd suggest that there is an affinity between how Birdman's ego-slaying queen of spleen and British critics would react to "interlopers" such as Riggan.
After all, Daniel Radcliffe, who took the lead role in Peter Shaffer's play Equus in 2007, had a mountain to climb to convince reviewers after Harry Potter, and Star Trek's Patrick Stewart openly fretted about his reception: "I was very fearful of the 'who-does-he-think-he-is?' response," he said. "'After 17 years in Hollywood, he thinks he can swan back to the RSC and give a performance equal to the work that's been done all those years he's been gone!'."
But the idea that one single review might close a show? There an Atlantic gulf opens up. It's true that a chorus of critical disapproval in London will drastically diminish a show's chances of surviving and thriving.
An appeal to fans to ignore the naysayers couldn't turn the tide of negativity that engulfed Viva Forever!, the Spice Girls musical, in 2012 and saw that it sank within eight months; The Lord of the Rings musical - at 25 million ($49.6 million) the most expensive in West End history - was another high-profile victim of a critical mauling in 2007 ("a thumping great flop", according to the Telegraph's Charles Spencer). Sometimes, as with Les Miserables, a set of mixed reviews fails to dent public curiosity ("a witless and synthetic entertainment", said the Observer) and with hindsight looks ill-judged.
Sometimes, very rarely, as with We Will Rock You ("Prolefeed at its worst", the Telegraph railed, in common with other papers), the show's target audience is so large it's critic-proof.
The advent of the internet and social media has helped shows bypass the "legit" reviews more than ever; the marketing campaign for The Book of Mormon flaunted Twitter "vox-pops" from happy punters, and ignored old-style review quotes.
But in London the press-pack is still eyed with a mixture of neediness and wariness by producers. It has never been the case, however, that one voice alone could bring a show to a premature close.
In the Big Apple, it's still held that the New York Times is the bible to which all good theatregoers refer for the commandment to book or not. Frank Rich disliked his epithet "Butcher of Broadway", which he suggested became official in 1986 - after Rowan Atkinson held him responsible for the demise of a revue he had brought to New York.
And David Hare weighed in too with an open letter about Rich's savaging of The Secret Rapture.
But in his collected criticism, he maintains: "The power of the job was not so vast as the Butcher of Broadway gags would have it. While I would not dispute some areas of the Times' influence - especially its critics' ability to encourage extended runs (or commercial transfers) of plays in off-Broadway or out-of-town venues - the power to control the fate of that most endangered species, the drama on Broadway, is close tonil."
Does that kill off Birdman's credibility? Not really. We want to believe otherwise, Rich argues.
So we will: "Why should I even bother to argue my case?" he writes. "The myth will never die."
Thanks to this film, it has even been given a new set of wings.
