In the movie that put him on the map, the great “Wet Hot American Summer” (2001), David Wain spoofed all those cheesy grade-Z summer-camp exploitation comedies from the 1980s, and the beauty of the movie was that it recreated what it was parodying with such derisive glee that it came close to being the thing itself. “Wet Hot American Summer” was awesomely smart about being awesomely dumb. Wain’s new movie, “Gail Daughtry and the Celebrity Sex Pass,” is a very different sort of comedy (and it’s not on the level of that droll classic), but it, too, is driven by a trash-in-quotation-marks double vision.

On paper, it sounds like a bawdy rom-com romp. Gail Daughtry (Zoey Deutch), a wholesome hairdresser in Wilbur, Kansas, is about to marry her former high-school-football-star sweetheart (Michael Cassidy). The two are devoted to each other, but like many couples, they have a deal that gives them a celebrity sex pass: If the opportunity ever arises, each of them is allowed to sleep with one famous person of their choice. Suffice to say that Gail finds herself on a weekend jaunt to L.A. in pursuit of hers: Jon Hamm.

In other hands, this could have been a plausible romantic comedy — a riff on love and sex and celebrity and fantasy and where all of them intertwine. But David Wain, who in 2014 made a scathing parody of rom-coms called “They Came Together,” has no interest in directing a “believable” comedy. From its opening moments, in which a small-town mailman (the always delectable Fred Melamed) narrates the story we’re watching with a note of unhinged hostility, “Gail Daughtry” has a tone that’s broad, antic, overemphatic, and a bit wacked. Everything in it is stylized and exaggerated, from the personality of Gail herself — Deutch plays her in a perky bob haircut and with a beaming smile, like a Sandra Dee character from the early ’60s — to the incident that sets off her L.A. trip: Gail and her fiancée attend a Jennifer Aniston book signing, and one hour later she finds him in the backroom of the bookstore…having sex with Jennier Aniston. (It’s at this point that we realize this is not a comedy set in the real world.) Gail must now attempt to sleep with Jon Hamm to even the score.