Well, here's a thought experiment: have you ever remembered something you thought you did, and suddenly can't figure out if you dreamed you did it or if you actually did it and just don't remember clearly?

Does that mean that dreams are just as real because we remember them clearly?

I'd argue that we view memories differently when we realize they were imagined. Thus there is some external value we place on the accuracy of history that has nothing to do with whether it's recorded or remembered. Recording and remembering events is not what gives them authority, but rather those are the best way we have to confirm they actually occurred.