Probably the print they used is the same one that was put together back in the late 70s for NBC. Keep in mind that the Saga was specifically made for network television, not for theatrical or video release. Wouldn't be worth them making a brand new cut just to show on AMC.

From wiki:

[In 1977] Francis Ford Coppola asked his editor Barry Malkin to make a 7-hour version for television. .....Malkin also toned down the violence, sex and language for a television audience

There are, however, two other versions which were uncensored

The Godfather 1902–1959: The Complete Epic

The Godfather 1902–1959: The Complete Epic is a reduced, 386 minute version of The Godfather Saga (434 minutes) that was released to video in 1981.^[5]^[6] Lucia Bozzola wrote of this version, "With the freedom of home video, The Complete Epic reinstated the violence that had been edited for television; free of commercial breaks, the narrative drive of Part I was mostly restored, but the impact of Part II was still muted by the separation of Vito's rise from Michael's descent."^[7]

The Godfather Trilogy: 1901–1980Following the release of The Godfather Part III in 1990, Coppola, Barry Malkin, and Walter Murch edited the three Godfather movies into chronological order to make the film The Godfather Trilogy: 1901–1980. As had the earlier compilations, this film incorporated scenes that are not part of the theatrical releases.^[8] It was released on VHS and laserdisc in 1992; it has not been released on DVD, and is now rare.^[8] The total run time for this version is 583 minutes (9 hours, 43 minutes). Reviews of this version of the film were favorable.^[9]^[10] An unsigned Time review reads, "This trilogy has a novelistic density, a rueful, unhurried lyricism and a depth that, singly, the films could not achieve. Altogether glorious."^[10]

Be nice if the last one got an HD or Blu-ray release. That would pretty much be the definitive chronological version since it also includes Godfather III.