This is not how I'd understand it.
From Cambridge dictionary: https://dictionary.cambridge.org/dictionary/english/fact , "something that is known to have happened or to exist, especially something for which proof exists, or about which there is information"
I'd also argue the words "known", "proof," and "information" all require interpretation as well.
* "something that is known to have happened" - Yep, 9/11 did happen. And some people say they KNOW that it was an inside job.
* "especially something for which proof exists" - job of the CIA is to exactly prevent such a thing, they did not.
* "or about which there is information" - come on. I won't link conspiracy theory websites here.
So, in the end, your definition does not contradict that someone calls the 9/11 conspiracy theory a "fact".
The first point is debatable - but then you could apply the same logic to WW1 or any other history event.
Therefore, I don't like your definition of fact.
> Job of the CIA is to exactly prevent such a thing, they did not.
This is not a proof that 9/11 was an inside job. Alternative interpretation: they did not do their job well enough.
TLDR; The discussions around "facts" are totally useless to me. Unless you accept that someone who pushes through their "facts" does nothing else than pushing their worldview onto you. Everyone is free to learn "truth" through their own perception. Other people's "facts" don't support this much.