In Britain, the phrase “off color” has always indicated that someone might feel under the weather because the color of their skin has changed from its normal hue to pale.
In America the expression “off color” has a related but different meaning.
When someone says something that is considered sexually shocking or impolite, it will often cause those listening to blush from a rush of blood that changes their skin color to red.
So the story that caused the skin color change is referred to as being off color.