Keith, the BoI system was not biased in favour of anybody or anything, other than to discover the reasons why an accident happened and what should be done to avoid a recurrence. It was the Airships of which you speak, or at least a number of them, that ensured bias by directly subverting them when they thought it necessary for whatever reasons.
As to the BoIs themselves they were only as good as the information to hand. Mull is an excellent example of this, as has been pointed out already. Although the BoI did not produce the finding required of it (some moral courage at work there I would surmise) it still did not investigate what is now generally regarded as a major factor in, and possibly cause of the crash of Chinook HC2 ZD576, ie its Gross Unairworthiness. It did not do so, probably because it was ordered not to, and certainly the man best qualified to inform the Board of the UFCMs and FADEC u/c runups, rundowns, and shutdowns, Sqn Ldr Burke (the Odiham TP), was not called and was ordered not to approach the Board when he expressed his wish to give evidence.
The problem about BoIs is that the system can shut down on them, and they become the proverbial mushroom farm. No matter how sincerely they try to do their duty (and I'm sure that they invariably do), if the RAF/MOD wants/ doesn't want a particular outcome then it, and not the BoI, will prevail. That's no way to run Air Accident Investigation, civilian or military, because more people die.