This is purely anecdotal, but it is my impression that while it's not uncommon for people to honestly (mistakenly) make a false assertion it is fairly uncommon for people to lyingly (and accidentally) make a true assertion. If this anecdotal data generalizes, it supports the idea that people who are lying more often know whether what they are saying is true than people who are speaking honestly. So if we had a reliable way of telling when people are lying, this would be quite helpful with getting to the truth.
Assuming my speculation is right, I wonder whether there is some level of assertion—say, speaking with confidence—such that when honest people engage in that level of assertion, they are as likely to know whether they are speaking the truth as liars are.
None of this is praise of liars. I suspect that this is largely a function of the sorts of situations in which people find lying useful.