"Is it possible that personnel would give false testimony to a BoI?"
The answer is "yes" but the more likely scenario, and one which clearly occurred in the two Boards of Inquiry I mentioned above, is;
a. The Board don't ask the correct question
b. They don't follow up or dig deeper when the answer is clearly rubbish
c. "Witnesses" know what the correct question is and withhold relevant information
d. Information/records go "missing"
e. The existence of such records is denied in the first place
Why else would a supposedly knowledgeable BoI, who can order staff to seek out answers, release a report stating that, for example, a system which they note as a likely cause of the crash is unfit for purpose and doesn't remotely comply with airworthiness regulations, but not ask questions like "Why was it fitted", "By whom?", "Was it trialled properly?", "Did the ADA appraise it (as it was a Service Engineered Mod)?", "Were pilot training and operating procedures updated?" and so on. Not to ask ANY of these questions is negligence. Or collusion.
But, worse, when all of the questions ARE answered after the BoI report is issued, and are entered into the official record, why were they not addressed at the inquests?
I concede not all BoI are conducted this way, perhaps very few, but the common denominator (to me) seems to be the protection of senior people who were forewarned but did nothing. It was, essentially, performance (in these cases, safety) being knowingly traded out - and one should ask why, given time and cost were not factors in either case.