The mind creates all kind of protections to help them cope.
I would say that is a very simplified, narrative-oriented perception of certain extreme responses to trauma. From a cursory googling, I see the movie in question is refering to traumatic exposure to violence in childhood. Yes, in situations such as these, some children develop psychological defense mechanisms, which may confer a distorted view of reality.
Defense mechanisms don't really function in the extreme way generally shown in narrative, though. There are many documented defense mechanisms, all of them have their own unique characteristics, and all of them can vary in intensity. It's also vital to remember that not everyone who survives a traumatic event, no matter how violent, will develop post-traumatic symptoms.
[T]he mind takes random information and forces it to support that narrative.
This is less post-trauma, and more the purview of cognitive psychology. Cognitive distortions exist and are quite common. How common is a matter of some controversy. This particular statement describes a kind of confirmation bias, which manifests as overconfidence in one's own views. It is not particularly related to trauma, as far as I know.
Overall, I would say that the kind of extreme reinterpretation of facts that is suggested by the quote you posted, is not a common thing. Reactions of a similar tenor may be usual, but as always, reality is more ambiguous than fiction. I would not call this statement fact so much as a directed or tendentious interpretation of facts.