I also heard the piece this morning. Despite being 22 years old the report probably still has some truth in it, but it is also somewhat overtaken by events in that the BOI system has been replaced by more independent Service Inquiries. I know that the previous system could (and did) suffer from intervention by convening authorities, but I think that problem is largely removed under the new regime.
As for the need for specialist investigators, AAIB support is available for all air accidents, but there will always be a need for investigators who understand the operating environment sufficiently to reach a properly informed judgement - for example, an ATPL(H) who has spent his career on North Sea rig-support might not be best-placed to investigate an accident that occurred in brown-out and under fire in the sandpit.
Do we need better trained investigators? Probably, but that is where the specialist external support should come in. However, the BBC assertion that the Nimrod airworthiness issue wasn't uncovered until the Inquest is plain wrong - the BOI came squarely and correctly to that conclusion and it was acknowledged in those terms by the CINC at the time, who stated that the loss resulted from quote "shortcomings in the application of the processes for assuring airworthiness and safe operation of the Nimrod." (check out published BOI on the MOD website).
Don't get me wrong here - I am not trying to defend what went on in the past, especially where it concerned senior intervention, and I do not want to get swept up in the Nimrod or Chinook debates. We just need to remember that the investigatory environment has already changed for the better. I would still prefer to be judged by my peers if ever I am on the wrong side of an accident, provided that those peers are suitably guided by experts in the investigation itself. And if I find myself on the end of an intervention by Air Mshl X based on something he heard down the pub, I will be the first to protest.