Think about how many details happen in your protagonist's world, constantly, that they are experiencing every day. For the story to fully cover everything your protagonist sees and hears in a day, that would require covering 24 hours of footage per day that the protagonist experiences.
Showing everything in perfect detail that your protagonist is seeing in a documentary is just a subset of that. You don't want to ever show every detail of what a character sees/hears/experiences just for the sake of showing every detail.
Instead, only show the snippets of what they're watching that are relevant to the story you are trying to tell. What's relevant to the story? Well, you should know why you have them watching this documentary as part of this story. What purpose does it serve? Once you know that, then that pretty much answers the question for you. Only show details that further that purpose.
Example: maybe the purpose of them watching the documentary is to give a sense of foreboding. Later in the novel they're going to be mauled by an alligator and so you have them watching a documentary about alligators. In this case the purpose of you having this documentary in the story is a sense of foreboding; therefore: only show details that give a sense of foreboding. Maybe a snippet talking about how the alligator can slip up on people unawares. Footage of its jaw crushing a massive bone. Something like that.
Hope this helps.