As a USAF trained aircraft mishap investigator, I can tell you that the HUD vid, while not classified, is often not released outside the USAF - not for security reasons necessarily (although that is much easier to explain to the public), rather, for the concept of privileged information. Priviliged information, as it pertains to safety investigations, means that only persons with a need to know, narrowly defined as those who are able to learn lessons from it (ie - the aviation community & leadership), are allowed access to it. This is very difficult to explain to the public at large as it smells very much like cover-up, when it's true purpose is the very noble effort of mishap prevention. Unless aircrew can KNOW the safety investigators are not going to hang them out to dry, or worse, be promised confidentiality by the investigators and then hung out by leadership for political expediency, then they will not be open & forthcoming with preventative information.
This came to a head here in the US during the Blackhawk shootdown previously mentioned. Then Secretary of the Air Force, Shiela Widnall, wanted to do away with priviledged information in safety investigations - this caused no small amount of consternation & was fortunately never brought to fruition.
Unfortunately, well-intentioned people often leak safety privileged information to those not authorized. This information is then used against the very people it was provided for to protect. It is my belief that this is what happened in this instance. I'm not saying aircrew who c*ck up should get a free ride if they turn "state's evidence", but that is not for the safety investigation to determine - that's precisely why we have two completely separate investigations.
That said, during the public investigation, factual evidence is made available from the safety investigation. The HUD vid would have been one such piece of evidence - most likely accompanied by a transcript that showed what freq everything you hear is transmitted on (so there would be no conjecture on whether something was in-cockpit, inter-flight, or external). The decision to release this is retained by the board president on advice from a military lawyer. Many, many times, this type of evidence is not released with the report, but transcripts nearly always are. Understandably, there is often not much press when these are "released to the public."
I do not presume to know how this investigation(s) was handled, any decisions to release/not release, nor would I likely ever be briefed on it - as I don't have a need to know being a non-CAS platform. I just provide the above as background info so you might understand how our BoI-type investigations operate.
Being told there was no video can mean different things too. It could be that the USAF/DoD conducted both investigations, decided not to include the HUD vid in the publicly releasable investigation, handed said report to the MoD & said, "Here's what we came up with." So when the MoD told the widow there was no vid, perhaps they weren't necessarily lying (lying implies you knowingly state a falsehood) as they were not aware of any video.
Perhaps, the Mod knew the vid existed, but the USAF refused to provide it. It may have been that well-intentioned MoD folks wanted to prevent any further undue strife by simply telling her there wasn't any video.
I am not saying that's what happened, I'm merely providing for the "reasonable doubt" before we lead everyone off to be hanged. Nor am I defending anyone who may have willfully lied. Well-intentioned lies are some of the most dangerous...
As for "private viewings" - several aircrew have gone to jail for that. One somewhat infamous incident involving Martinsburg, WV ANG C-130 that did some impromptu low-flying caught a powerline & were unable to climb out of the valley they were in - knowing they were going to crash & die, at least two of them left messages for the families during the nearly 5-minutes it took before they impacted. Squadron members got copies of the CVR and brought families in to listen to them - they were dealt with very harshly.
The concept of privileged information is often hard to reconcile with bereaved family members. What is morally right for one person vs an entire Air Force is potentially in the balance. For that portion of our "closed system", there can be no compromise in my mind; that's why we have two investigations - one for prevention, one for disclosure - they're never identical and often have differing opinions.
FWIW, I believe we, as aircrew who have a need to know, should be provided full-disclosure crosstell in these safety investigations.