"The the same dancer will not dance it exactly the same twice running."
While we want to leave room for intentional interpretive variation, being able to intentionally achieve a high degree of consistency is also an important dance skill, and something that often sets professionals apart from amatuers (even if they are wrong, they are consistent about it)
"If there are differences how can anyone tell unless the music is playing. If there is no time signal to let you know when the step commenced how can you possibly measure it."
You can measure the TIME BETWEEN STEPS. If that is at odds with your theory of how they are supposed to fit the beats, then obviously your theory cannot apply to the dancing being measured.
For example, if your measurement of the time between two steps is not a whole number of beats worth of time, then there is NO POSSIBLE WAY that both steps can be falling on beats (unless the music itself is uneven). Either one is on a beat and the other isn't, or neither is actually on a beat.
You don't even need to turn on the sound in order to deteremine what the time value of a beat is - it's enough to measure the time between comparable steps in successive measures, and divide by the number of beats per measure. If the dancer is any good and the tempo unvarying, you'll get the same answer for many measures in a row and thus have a high confidence in your calculation for the amount of time per beat. That's how I can know exactly how long a beat is on Sinkinson's foxtrot video - because his timing is extremely consistent for FIVE succesive measures of SQQ material all captured by the same camera.
Or to return to waltz: if I watch Jonathan's video and I see that when his foot closed it is 1 beat worth of time since step 2 was placed, and 2 beats worth of time since step 1 was placed, I know that either:
1) Step three arrived closed only on beat three, NOT BEFORE
or
2) The first two steps were not on the corresponding beats. Which would be rather suprising!