I'd have to say for me, I can see reasons for each. For BR, no further thought is required on my part. Her only intent was to protect her young son from the devastating process of being held responsible publicly for his sister's assault and murder.
With JR, each parent had to have something to lose. If JR was molesting her and Patsy bashed her skull in a rage, they each had good reason to protect the other.
With JAR, I can't see Patsy covering for him alone. BR would have to be involved somehow. I don't care how much she loved her husband and her lifestyle, I don't see her covering for her stepson and just letting it go.