It is a natural inclination for the body to sway to music. Musicians sway all the time when they play their instrument or sing. Some do it a little more heavily than others. When training in classical singing, we’re taught to be more poised while we’re singing because it can be a distraction if one moves too much during a vocal recital for instance. BUT there is still the natural movement that goes along with the rhythm of the music. If you watch ensemble groups, you’ll notice how many of them will move around the same moments within the music, whether or not each individual musicians is a heavy sway-er or a more conservative sway-er.
Here are some examples of the natural swaying inclination based on the music and the text of the music:
Watch the male and two females soloists close up and then when there is a far away shot. Also watch the orchestra members, then the choir, then back to the three males soloists together and see how they “dance”, or “sway”:
youtube.com/watch?v=VoKZ5KSsCsI&feature=related
If this is the kind of “dancing” referred to, it’s not really dancing per say. I sway like this when I perform or just singing hymns in congregation.