A cracked mirror can still tell the truth; it just makes the truth harder to recognize.

Damaged sources can still be accurate. A person with obvious problems can be right about you, a flawed account can contain the essential fact, and dismissing the whole thing because of the distortion means losing the part that was true. Sorting is harder than rejecting.

When information comes from a compromised source, look for the specific claim rather than judging the messenger. Ask what would have to be true for the useful part to hold. Then keep that and let the distortion go.