That's quite a hypothetical situation that you posit, with "a thought I must conclude is from outside my own brain", with "demonstratable facts", and "a purported source". I suppose I could well waffle about "the "thought" itself, the "facts", the "demonstratable to whom" idea and the "source" until you toughen it up some more but, with the presumption within the question itself, there's little point.
Would I conclude Goddidit? Satan? The Trickster Coyote? No, no, and no.
Would I conclude I was going insane and ask for medication? No.
Would I conclude there was a person or alien with projective telepathic abilities hanging around warping my thoughts for some unknown purpose? Probably not.
Do I have a definitive answer to this hypothetical question? No.
Does that bother me? No.