You don't have to believe it, it's been confirmed by them and Tatler wrote about it as well.
And yes, BP, KP and CH work in isolation very often and sometimes work like 3 separate courts instead of one central court under BP or StJ, which has caused a number of issues over the years and efforts to bring them together (this was publicly commented upon as recently as just before Meg came onto the scene).
BP isn't some super power with Liz knowing every move within its walls. There's loads of staff there etc.
I don't know why they'd talk about it in the docu, fact is they did and fact is it's been made with the cooperation of KP and fact is that tidbits like these always tell you the real story instead of the glossily spun PR fakery they put out.
It's well known who the ring was left to, as people were present. When the story is "H gave the ring for K" it's all sweet and thank God it's not on M's finger, but when W's selfishness comes to light it can't possibly be true.
The ring wasn't left to the next in line or to the throne or whatever, Diana specifically wrote that all her possession are to be left to W&H, the jewellery for their wives to be worn and chattels to her godchildren (this bit was ignored and her godchildren received trinkets after fights in court). Nothing was left "to the crown" or someone specific in the line.
Also the Winds were notified a couple of hours before the press, so yeah plenty of time for Liz and Chuck to give the palace key "to let the press in".
Can't believe that a straight confirmation from the horse's mouth won't be taken as "real", because "Will's too respectful and good"