I can't see how that would be so.
It is true that an extrovert is more likely to be highly social, and an effortless conversationalist, but that by itself doesn't make them glib or dishonest. It just makes it easy for them to "put out" and actively engage relative to an introvert.
Indeed, if there's ever been an unfair trope out there in the wild, it's that there's something inherently "wrong" with introverts, that they are withheld because they have something to hide, or are in some other way suspicious, because they don't "act right" from an extrovert's point of view.
As an extrovert, I find it easy to talk with people. This doesn't automatically make me a liar. Lying is about a person's character and values, not their conversational ability.
"Six Reasons Why People Lie When They Don't Need To"
I agree. I don't think that aspect of personality would have anything to do with it.