Edward Snowden, WikiLeaks, the Pentagon Papers—it seems like Americans get a chance to peek behind the surveillance curtain only when somebody commits a crime. That precedent was arguably set on the evening of March 8, 1971, during the “fight of the century” between Joe Frazier and Muhammad Ali, when activists broke into an FBI office in Media, Pennsylvania, and stole every file they could find.

As the activists sorted through documents to mail to journalists, even they were shocked to find that more than half were dedicated to spying on activists and undermining draft resistance. (An estimated 1 percent of the FBI files were about organized crime.)

It was the public’s first taste of a surveillance state that has become depressingly familiar. The FBI never figured out who was behind the break-in, but some of the burglars came forward in 2014. This plain but very informative documentary fills out the details of who they were (mostly college types, including a physics professor), what they did, and what happened afterward—including the revelation of J. Edgar Hoover’s COINTELPRO campaign to “disrupt, misdirect, discredit, neutralize, or otherwise eliminate” political movements and their supporters.

As Frederick A.O. Schwarz Jr., chief counsel of the Church Committee—a Senate investigation into state surveillance—concludes toward the end of the film: “A government program of secrecy and no oversight is bound to have mission creep and go from the wrong but understandable to the horrible and un-understandable.” We just don’t learn, do we?