No, it doesn't. You are confusing the difference between cause and effect. time only remains constant because time pieces are calibrated using the same standard. If you take two wheels and spin them at the same rate and stop them at the same instant then their circumference will have travelled the same distance. That tells you nothing whatsoever except that the experiment fulfills the criteria you have set. You have caused the phenomena which you observe by setting finite constraints.
Watches and timepieces only measure the accuracy of the timepiece. When you constantly re-adjust time pieces to reflect ONE single standard then you are controlling the variance of what exactly?
When you measure distance travelled by the amount of time it takes to travel from a to b at a given speed then ALL the constraint are set by reference to the same point.
It doesn't say that the point is an accurate depiction (well, only for a given value of accuracy)
If you measure a twelve inch stick with a twelve inch rule can you guess what the measurement will be?