Back when the roster of acts at Woodstock was being assembled, the organizers considered very seriously whether they should invite the Rolling Stones. In the end, they decided not to, although probably not for the reasons you might be thinking.
Much of the planning for the festival was predicated on the idea of keeping mayhem and violence to a minimum. "Their hit song at that time was 'Street Fighting Man,'" said concert organizer Joel Rosenman a couple decades after the fact. "And we just didn't want street fighting in our festival."
Well, in reality, "Street Fighting Man" was a hit in the summer of '68, not '69; its release coincided with the Democratic convention. (In the summer of '69, "Honky Tonk Women" was the Stones' big hit.) And it wasn't even a hit, really, peaking at Number Forty-Eight. But given what happened at Altamont, Rosenman may have been right anyway.