In the context were talking about, I would think that the two usually go together - at least, there won't usually be a conflict of interest unless there is a vested interest (even if on behalf of, say, an employer).I think you're confusing 'vested interest' with 'conflict of interest'.
The world is full of 'experts' and I seriously doubt that one could not have been found. For example, I sometimes work with an organisation which has a whole department full of 'experts' in relation to all aspects of fire hazards and fire investigation.Where do you think they might have found an independent expert with sufficient knowledge to add to their discussion?
In any event, as I said, at the very least, it would probably be appropriate to have the report of the LFBs investigation reviewed and assessed by an independent person - as regards methodology and the correctness/ appropriateness/ reliability of conclusions, something which does not necessarily require specific detailed knowledge of the subject area in question. I have provided more than my fair share of such 'independent assessments' over the years!
Kind Regards, John