I had seen the documentary film, plus read a few stories written about this shoot. The monarch had hired AL to do the work. They paid for the shoot. That being said, AL did have her choice of gear to use for how she wanted to capture things. At that time, the 1DsMKIII was also being introduced, and she appears to have had one in the kit, though the final shots were evidently captured with a 1DsMkII. (You can see the different sized LCDs in parts of the film for openers.) AL's team/entourage rented most of the other lighting gear and stuff locally, rather than haul so much around. She could have used anything she wanted, but has been using Canon stuff lately, mainly because of the freedom she had to do scouting shots and things like that. She used the 24-70mm f2.8L zoom lens because it gave her the last second creative composition power over a fixed lens and having to move everything around. She did shoot tethered, but worked from a fairly fixed spot that had been rather extensively prepped for light control. On some of the other shots, there was a lot of compositing done to get the various lighting looks needed to capture the vision she wanted.
At the time of this shoot, the more modern MFDBs were just starting to come onto the scene also, and many had not yet gotten rave reviews for performance or file handling as we have available today. Also, there was a big issue about not wanting what had been the "traditional portraiture" type of shot, where MF film had been used almost exclusively by the Queen's photographer. A lot had to do with the ability to composite shots with various exposures, and the DSLR was already a decent and rapid tool for this sort of shooting.
Anyway, that is a bit more of the background that I gleaned from this. Personally, I did not think the shots were outstanding as others from AL have been, but she did capture a very different perspective and interpretation of the Queen as nobody else had really done, so it was effective. Would it have been "better" with a MF rig? Evidently AL did not think so, feeling it was more limiting to what she wanted to do. Folks with argue this till the cows come home, but she did it her way and it worked for how she envisioned things, and that is what matters.
LJ