I agree with you about the parry; it can get you into trouble. If you watch the DLH v Ruelas fight, the first knockdown comes after Ruelas reacts to a DLH feinted jab to the body with a sweep of his right hand. Personally I would just ease back, get barely out of range of his jab.
And a jab to the body is a great indicator of distance. If you are a taller fighter, getting low and jabbing to the body will keep a pressing fighter away from you. As you said earlier, you can't slip a jab to the body.