If the story isn't about the fact that a character is lying and we're telling a story about liars here, then the lying of the storyteller — or possibility of lying — undermines pretty much one hundred percent of my ability to suspend disbelief. I'm willing to go with you if the apparent veracity of the story doesn't vacillate — always fairy tale, or always journalism — but when you introduce the "but wouldn't it be so cute if this wasn't actually true?" question, my answer suddenly becomes "fucking no it wouldn't you dick," and now I'm not even sure if I can believe anything you've said.
The trope of someone who has left out some crucial detail of their past, which is later found out by the main character, comes to mind. "Everything else was true! It was really me! It's just that I'm not really Space Ghost, that's all!" Or whatever. They may be telling the truth now, but the main character has no way of knowing that, and is now dubious to the point of feeling betrayed and pissed off. To some degree, the thing they thought they were both participating in equally wasn't actually true. Is it just that they're not really Space Ghost, or could it be more? And how could you believe them even if they told you?
I'm not advocating throwing the baby out with the bathwater, but that's how I react. And the only way this gets resolved is if there's (very quickly) a resounding answer to the question. If they immediately go "no no no, bad joke, sorry, I'm kidding, it's real" I can ramp back up some trust before the credits roll. If they leave it at the question, peace out.
