I think your sentence is accurate if you replace the word "factual" with "accepted". But in public discourse some people tend to want to use the word "factual"

I think your sentence is accurate if you replace the word "factual" with "accepted". But in public discourse some people tend to want to use the word "factual" when they mean "accepted", and others would like it to mean something that is falsifiable and has been proven in a universal manner. Thus this argument is reduced to semantics.