There are a subset of patients who did have inflammation in the brain.
But the vast majority of people with chronic fatigue don't.
There may not be sufficient proof of the positive, but I've never seen positive proof of the negative. (Is there? I checked with a neuroscientist and he said there is not.)
I wish doctors understood logic, probability, statistics and causal inference. I wish the public (and TV documentary producers) didn't mistake doctors for scientists.
I would never have put a statement like this in a film because it's factually wrong. And that's the challenge with experts in documentaries: they often misspeak. But you still need to be able to make sure that everything they say can be cited. If not, you can't include it, no matter how useful the scene may be otherwise. This doctor misspoke, but they didn't have the technical expertise nor the rigorous fact-checking process to catch/care.