Again, I do see your point. But at the moment, and for the forseeable future, it isn't independent. Given that to be the case, how can the deckchairs be re-arranged to achieve the best possible outcome. Despite the failings of the past, I hope (and believe) that the situation is very different now and that such a situation could not occur in the same way again. Surely what matters is to do the right thing, not to appear to do the right thing.
By that I mean that physical independance for an authority or an investigation body can be achieved without actually happening in reality.