You can't make sense of accidents either, not that Burke didn't intent to hit Jonbenet just didn't expect the catastrophic deadly results.
I think Patsy was covering for Burke but John was covering for JAR and his molestation of both Jonbenet and Burke. Both kids had the regressed toileting problems. JAR is by his age alone more likely to have been involved in molesting or 'experimenting' with both sexes, molesting both children.
Look at Burke today, he's not even matured into a man, he's immature and child like or as Dr Phil calls it, 'Socially Awkward'. His daddy is fighting his battles. He works alones, lives alone, something happened very early in his childhood ages1-5 for this kind of result.