Dreaming

So, I heard once that a psychiatrist came up with the idea that maybe dreams didn't really happen during the night.
That we weren't spending a good chunk of the night watching movies in our head.
He thought that maybe what was happening is that our brains were firing all night, and when we woke up, we attempted
to interpret that neural activity, and that gives us images and memories of SOMETHING and we call them dreams.
Then he decided that from a therapy perspective (dream interpretation) it didn't really matter.

Anyhow, I was thinking about that for some reason.
It would, I think, help explain why some people remember their dreams and others don't.
It would, I think, help explain why we tend to only be able to half-grasp dreams, especially if we wake up and start moving.
What it might not help with is lucid dreaming.
For those who don't know, lucid dreaming is when a person is aware they are dreaming, and often they have a certain amount of control over the dream.
What's interesting when you combine these two ideas, is that you come to this juncture of experience (objective) vs memory (subjective).
How could you know?
And how does this sort of idea affect who we are as simply a collection of memories?