The throttle clamps to the bar perfect, it's the grip that rotates. And it is only on some of them.
My Murray stays put, my old Trail bronc has the original grips on it stays, it's the newer aftermarket Taiwan ones that move.
I have a reall nice set of HD aftermarket grips that have the foam and chrome on them, they seem solid, don't really own a bike that requires "chrome" but they are cool.