It's a really puzzling question. I've wasted a lot of brain cells on that one.
Question: Are they consciously aware of it? How do you prove that? Sure you can prove they are wrong, but can you prove that they KNOW it?
A common pattern I see around here goes like this.
Alice: "The sky is green"
Bob: "Actually the sky is blue"
Alice: "You can't prove that. I saw the sky, and it was green."
Bob: "Here is a photo of the sky. I used photo editing software to check the color of the sky. The color came out as (73, 131, 168) that's more blue than green."
Alice: "You used photo editing software, so you're admitting you faked it."
Bob: "No, I just used it to check the color. How about you send me a photo, and I'll check your colors?"
silence
1 week later...
Alice: "The sky is green."
Bob: "No I told you last week. The sky is blue."
Alice: "You made that up. It's all lies."