A fact is an item of knowledge, that is, a true belief that we are justified in believing as true. So by definition, a fact cannot be false. If a fact that was thought to be true is later found to be false, it is no longer a fact.
Since <em>distant:intimate </em>are words that have opposite meanings, you need to find another pair of words with the same quality. The correct answer is morose:joyous, because those two words mean different things.
