The reason I think an accident, or at least an unplanned act such as hitting P too hard or something like that, is possible is because MJ, especially, since he was in the process of moving out, would know that LE might not believe it was not on purpose. They might think he was acting out of some sort of revenge about the end of the relationship, or having to move. And if someone else was there as well, i.e. cousin, then I can easily see them panicking, huddling, tossing out suggestions and ideas, etc. and thinking no one will ever believe it was not on purpose.
And then once the case gained steam, it was too late, in their minds, to try to explain what happened. They locked themselves into a story, did the prick-your-finger blood brothers thing we did as kids, or whatever, and swore to stick to their stories. If so, I'm sure they are sweating big time every single day, as they should be, for depriving P's family of having her to put to rest. But I'm not sure we will ever really know for sure unless she is found, and even then, only if the location can be linked back to someone.
(This is all supposition, obviously, but I can totally see it happening.)