It is entirely plausible that our mind connects these fragmental sensations into one coherent and continuous story. One doesn't know that the dream was like a "video", since our mind automatically fill in these gaps (sort of like the blind spot of the eye), and we can't know for sure what was dreamed and what was filled in, no matter how convinced we are.
Even in ordinary life experiences our mind strives to make sense of it all (the sensations), it orders and structures them into a coherent pattern. Bad eye-witnesses of crime scenes is a good example of this. Some can remain absolutely convinced of their perspective of the details of what happened, even though they are entirely wrong. The important part is that they remember it, even though it never happened. It is all due to how we subconsciously force incoherence into coherence.