Originally Posted by Puppycow
No, not quite. Their steps and movements may be choreographed, but they still have to follow the rhythm. If the music is not pre-recorded, the orchestra may change the speed slightly. There is also improvisational dancing. And in ordinary partner dances, the woman (usually) has to follow the man who's leading, while also keeping steps in sync with the rhythm of the music.
Over the years, I have watched many women being led by men who were out of sync with the music. They are often very good at hiding how frustrating the experience is.