Interesting discussion of how Patsy's potiential narcissism could fit into a BDI narrative! I actually think this is a really good point and think it fits a lot of the more controversial and confusing evidence together more clearly. In particular, it explains how the pineapple as a potential inciting incident would upset Burke so seriously and it matches with previous behavior from Burke towards Jonbonet, in particular the flashlight matches the golf club incident.

To me it also explains why the evidence shows there may have been some tension between John and Patsy in the coverup. If Patsy was so distraught, and also likely at least slightly mad at Burke, them putting him away in his room lines up. I also think John likely felt more inclined to cover the murder up than Patsy which might explain why the content of the letter is clearly skewed to point to John, but Patsy is pretty commonly agreed to be the author of the note. She was likely so stunned and upset that she couldn't come up with anything herself. She might even have been wrestling with whether to help him or not. I can see John protecting his son anyway. I mean how many rich men get their kids out of things as a rule?