The story of Anthony Weiner and his fall from grace has been reduced to caricature epitomized by puns that write themselves to such an extent that it’s easy to forget the actual human at the center of the scandal.

The documentary “Weiner,” in which filmmakers Josh Kriegman and Elyse Steinberg follow the former congressman during his ill-fated 2013 mayoral bid, serves as a reclamation project of sorts.

The film inspires a reconsideration of closely held beliefs about Weiner and what he represents, thanks to the extraordinary access granted the filmmakers to even the most intimate of moments during that summer, as a surge in early polls would be fatally wiped out by a resurgence of the sexting drama that drove him from Congress two years earlier.

The filmmakers engage with the frenzy that characterized Weiner’s campaign, capturing the early excitement through montages of various parades and other bits of retail politicking, scored with inspired soundtrack choices such as “New York Groove.” They are there, equally, for every bit of the madness as the scandal re-emerges with Sydney Leathers, apparently code-nicknamed “Pineapple” by Weiner staff, serving as a media-savvy foil.

There’s plenty here for political junkies, and even more for those fascinated by the behind-the-scenes machinations that propelled this improbable redemption story. Through immaculate skill, characterized by an eye for distinguishing the moments of significance from those of empty spectacle, the filmmakers have made a movie that defies the simplistic pleasures of watching a train wreck in motion.

They have, instead, through the uneasy blend of loud moments with scenes of soul-crushing quiet, crafted a film that takes the full measure of a man who has a lot more in common with the rest of us than one might think.