What if you have a fact that is a 100% lie? What if everyone knows? Don't despair. There are ways to make people act like they believe lies, even if they are explicitly told what the lies are.
To accomplish this nefarious act, all we really have to do is make them feel rushed and overburdened. Psychology researchers asked a group of people to look over summaries of crimes. The summaries contained false statements, but the statements were clearly marked in red. Sometimes the false statements exacerbated the severity of the crime, like the victim was an orphan wandering alone through snow, or the perpetrator used his stolen boots to kick a puppy. Other times, the statements provided extenuating circumstances: The perpetrator only stole the car to drive his laboring wife to the hospital; the victim was hit in the face, but only after yelling abuse at a bus full of nuns.
When the subjects had finished reading the reports, they were asked to give the criminals what they thought were appropriate sentences. Naturally, they discounted the false statements, but another group did not. The other group of subjects were given the same summaries to read, but were asked to read the summaries while searching for certain digits. Given two tasks to do at once, the subjects were swayed by the lies. If the lies were exculpatory, the criminal got a lesser sentence. If the lies exacerbated the crime, the criminal got a longer sentence.
The moral here is, people don't even have to believe your lies. If they're busy enough, they'll go along with them, because it takes mental effort to shrug off suggestions — even false ones.