Interesting video... You can see on how Charlie alternates drum patterns in a sequence of two bars. Probably he does this all the time, but it's new to me.
Not a musician and not educated in music at all, but it seems to me Charlie kept this up through 1971 performances of the song. It was a very different rhythm and one that allowed Keith (and later Bobby and Jim Price) to mimic Otis' arrangement while still giving Young Mr. Taylor plenty of room to improvise his solos. For once, Mr. Jagger was not following Mr. Taylor's melody lines but following the rhythm (based on Otis' arrangement) instead. It allowed for the glorious dichotomy of Taylor being deployed as a counter to the rest of the band. The same sort of tension-filled approach taken with "Bitch" and "Can't You Hear Me Knocking" in the studio that would produce such glorious results. Again, others may not agree. This is just what my untrained ears makes of it.
Charlie had that 1 snare 2 kick drum (and vice versa) from We Love You, I think, or perhaps even from the BTBUTTONS sessions with Dandelion, I think, through Dance Little Sister. He pulled off that for BLACK AND BLUE and then started with the not hitting the hi-hat during the snare with SOME GIRLS onward. I don't recall him doing that before.