Yes but your example contains some truth but isn’t true in of itself. The outright lie is where he is representing himself as the cause for low unemployment.
Cory is saying that if the shithole said “Unemployment is low.” and went on to say “I don’t believe it has any correlation to my presidency.” then it would fit your definition of a story, also be true and be from an unlikable source. (…and my first instinct would be to sneer and want look for some reason to dismiss his story as bullshit.)