"Anonymous. I you had a class and they all did a Waltz or a Foxtrot routine without music. Do you think they would all be exactly on the same step. If you say yes you are not in the real world, but in a world of your own imagination."
Actually it is likely that they would match each other to a suprising degree, because there are a lot of incidental cues to pick up on.
But let's assume that each couple did it's own thing. Would they be off time? Well, some would be off time because there movement was too erratic - nothing resembling what we think of as a waltz or a foxtrot could fit it. But others would be on time - you could easily compose a piece of characteristic music in response to their dancing.
One thing that this whole argument brings out is the two ways or relating to music. I'm going to borrow some engineering methods for these: sythensise of movement by discretely clocked samples, vs. phase locking.
The method you and some others here are advocating is the former - synthesis by samples. Because you lack an internal feel for the movements, your only recourse is to excute them piece by piece, as a discrete set of actions clocked out by the fractions of musical beats. In the case where you have nothing else to go on, this is not a bad way to start out approaching the problem. But it is crude and mechanical - and as was the case for the waltz rise, if you don't pay carefull attention to the exact meanings of the terms in your textbook, you can fill your table of what to do on what beat fraction with mistaken entries.
So advancing dancers get to the more sophisticated way of relating to the music: phase locking. Here the dancer/couple must already have a very good idea of what a unit of the dance feels like and be able to dance it with quite nicely "musical" timing without any external music. Add the music, and they do not listen to the beats. Instead, they listen to the trend of progession - approximately the measure level. Instead of worrying about the beats, what they do is match the trend of their dancing - the rise and fall cycle for example - to the trend of the music, as represented by measures. To put it crudely, they adjust until their drive is precisly in phase with that of the music - because that, and not lockstep robotocisms - is what the eye appreciates as flowing, musical movement.