I think at least half of the Bob Dylan songbook has to do with truth
and confronting liars in one way or another. Positively 4th Street and Like A Rolling Stone may be considered too searing for a service, but others I can suggest are:
My Back Pages. (Dylan anniversary concert on YouTube.)

Dark Eyes (Judy Collins version on YouTube)

And in a sense the 'protest songs' unearth truth in a storyline or metaphor:
Blowing in the Wind
Lonesome Death of Hattie Carroll
When the Ship Comes In
The Times They are a Changing

On the lighter side, not folk at all , but usually sung with a smile and a wink:
It's A Sin To Tell a Lie