Has there ever been a "Million Little Pieces"-type controversy in music?

Despite his image, Kristopherson was a Rhodes scholar.

Shania Twain represented that she had “Native American” roots because her stepfather was native American.

Practically every single note of Trois Gymnopedies by Satie was a lie. The proof of this is in Blood, Sweat and Tears’ cover in their eponymous album. The footsteps and closing door at the end are neither intended nor David Clayton-Thomas’ indignation at the lack of lyrics, but Fred Lipsius’ protest (he discovered the deception only in the studio) at the outrageous offense against truth his sax was being asked to perform. Among the more obvious lies: B-flat, B-flat, F, the entire sixth measure, and at least five of the half-notes approaching the end of the piece.

I’m not sure if it led to public scorn or disdain, but Bob Dylan’s “Hurricane” was certainly presented as an accurate and historical account which was later determined to be lacking objectivity in the very least and twisting (and omitting) certain key facts at the worst. It spurred at least minor controversy in the '70s. Interestingly, Dylan hasn’t performed the song since 1976.

Wikipedia’s take

Didn’t Ice-T claim to be affiliated with a gang he had nothing to do with? Does that count?

The Encyclopædia of Tlön (which was written on a planet that may or may not exist) recounts a dream of the ancient philosopher Meng-tse of three maidens who sang throughout the land and were welcomed in all festivities of honour. But when one of the imperial scribes dreamed that the three maidens were not maidens at all but oranges transformed into the simulacra of maidens by magic spells cast by the Turquoise Sorceress, and given the power of sweet song, the people were scandalized. The Emperor Hsiang decreed that the three oranges may never again perform in the realm because they had attracted the public by deception. And so they took ship for barbarian lands to the west. While reading this account, I recognized certain indications copied from the Hebrew translation of Averroës showing that the Turquoise Sorceress was, in fact, my granddaughter—who has not yet been born.