I am so not going to judge Burke on this. I can see how this can be spun as showing some guilt or indifference on his part but I can also see the other perspective; maybe the Burke perspective...the BPD targeted him, and his parents and failed his sister miserably. It's not Burke's fault that the BPD botched this investigation from minute 1. He has been asked questions and at a time when it was fresh. He may have a serious mistrust of the police - I know I do and I would in his case. And the smart thing to do is to have a lawyer - there's nothing cowardly about it - that's Lin's job and he is very good at it. Burke probably believes they are going to go down the same old path and try to implicate his parents again - or him for that matter. His entire life has been lived in the shadow of his sister's death and the umbrella of suspicion. Maybe he's just let go, had enough, believes JonBenet is at peace and with his mother and just wants to live a normal life. I can see that.
Not everybody handles things head on (I do, but Bless the hearts of the people God has put into my life to teach me that what I do and what I think should be done is not going to change how others deal with difficult situations).
I honestly don't think that HE believes the police want justice for his sister; I think HE believes they want a Ramsey to be arrested and tried. If I had that belief I'd tell them to go pound sand too...or rather I would have my attorney or family attorney speak on my behalf. That doesn't make my way right either, but I can see that perspective.
The problem with this case is that practically everything, if you are going to be very honest, can go either way depending upon your notions of who you think killed JonBenet. It's really why it is so frustrating for everyone.
I can see the RDIs being furious with Burke because of their notions. But I bet no RDIs can see the other side or even try.