A fact is only a fact if it is true.

Incorrect.

Facts are unchanging. Truth can change as it is our subjective interpretation of facts also coupled with our own speculations and hypothesis. Christians believe one truth. Muslims another. Hindus another. Scientists also have different truths.

Truth can change. Facts are the things that do not. A "car" hit a barrier. Car is a fact. Why the car hit the barrier would be a truth, and involve a lot of speculations.