If you think about it, is there really any difference between time running straight forward, time branching off infinitely, or time not actually existing at all to a person who is observing it within that theory?
In situation 1, which has a single, unbroken temporal reality, the person would observe time moving forward, and he would be correct.
In situation 2, with the fractal temporal reality, it would appear to the observer that time was moving forward, since he would have no way to observe the other realities.
And in situation 3, in which time does not really exist, and in which each moment is its own separate universe, the person would still believe that time was going forward.
Since we lack any way of viewing alternate temporal realities, we cannot prove the way time flows any better than the Greeks could.