Well, I stand corrected. Obviously, Ancient Aliens must be completely true since it is indisputable that ancient buildings actually exist. So, yes, there is a fact in Ancient Aliens, which means that by definition the program fails to be "fact-free." I suppose I should issue a formal apology to Ancient Aliens, but instead let's just agree that the show is mindless, lacking in even rudimentary critical thinking, and marred by lies and fraud.
But, yes, it does occasionally contain a fact or two, despite itself. If it had no facts whatsoever, it would be simple fantasy, like Lord of the Rings. A sprinkling of facts, though, grounds flights of fancy in spurious reality and makes the lies and distortions more plausible than they might otherwise be. Lovecraft understood this when he used carefully realistic settings to ground the Cthulhu Mythos in the milieu of New England, prepared with all of the care one would take in creating an actual hoax, though, Lovecraft said, "of course none of us [weird fiction writers] has the least wish actually to mislead readers."
Lovecraft was honest enough to admit his alien stories were fiction. Helena Blavatsky, L. Ron Hubbard, Erich von Daniken, Giorgio Tsoukalos, and David Childress have no such scruples.