Every false statement corresponds to a fact that the statement is false. More precisely, the concept of falsity depends on a prior concept of truth (false = antitrue, but to make truth into mere antifalsity would be metaphysically confused).
Axiologically, goodness is similar to truth, and evil to falsity (not just the absence of good, but its opposite). So the concept of good is logically prior to the concept of evil. There is an illusion in standard deontic logic, which is an inference from the formal interchangeability of the definitional scheme to the actual possibility of justifiably ordering deontic concepts using evil/the forbidden first---but this is abstract evil (it is wrong to base one's concepts of ethics on the concept of wrongness).
If, moreover, goodness is something like "acting according to the truth" (Kant says somewhere that this is analytically true but otherwise vacuous), then focusing on false statements would be congruent with focusing on evil.