Knowing JF, as I have had the privelege, I am damn sure he would have a quiet word wherever suitable if he thought it was required...
My only experience of AAIB / BOI was during very politically charged situations - those with a knowledge of the Harrier GR5 development will know what I mean, and a very short search would produce a relevant website.
In the case I'm thinking of, the results were very skewed indeed ( though eventually put right ) but that was a very different situation, see no reason why this sad accident should not be treated professionally and hopefully lessons can be learned in whatever way.
I saw the pilot's funeral on local TV tonight - all I can do is offer thanks to him for all the enjoyment he gave to so many people, up to the day, and sympathy for his family & friends.
I didn't see any mention of a flypast, maybe that would have been too painful.