Fact has no good antonym. Lie is a fine word, but it carries more than just a suggestion of intent. When someone lies, he's not doing it on accident. An accidental lie is just a misconception, but misconception is weak. It suggests a simple misunderstanding that can just be corrected. A fact has a foundation that can't be pushed aside as easily as that.
So, to fix this hole in the English language, I propose a new word. A faceit is an item of knowledge held to be fact in spite of a consensus of verifiable evidence to the contrary, an alleged event or circumstance with no observational evidence, often used as a foundational fact in constructing a larger incorrect view. Although a person may be aware that their larger position is disputed, they will generally be unaware of most of the specific faceits underlying that position.
By this definition, for example, homeopathy is too complex to be called a faceit, but the "Law of Similars" and the amazing properties of water do qualify. Astrology isn't a faceit; it's nonsense. It is a faceit that my birthday of July 6 makes me a Cancer. Creationists hold fewer faceits than you might expect; they're wrong mostly for other reasons. I'll save that discussion for later though.
People should be more aware of their underlying assumptions. If less of them were made up, I wouldn't have to make up words to describe them.