I've long been meaning to respond to this thread.
When I saw this doc just over a year ago, after a glass or two of Malbec, I was awestruck! What an amazing story!
However, it is not clear that Skinner got thru to Macca himself by phone; unlikely he would have his actual number and in a recent interview Macca himself said that it was his then-manager who told him the news of Lennon's death by phone. So maybe Skinner called up the manager, that sounds possible.
Then again, I also read that the first they heard of it was when Linda did the school run, and one of the mums told her.
Then there is the story that Yoko himself got in touch with Paul and the other Beatles, as related in Shout! Except neither Paul nor George verify this, unless it was a case of Yoko calling their 'people' to convey the news, rather than them personally. Harrison revealed on the Aspel show that he was called while in a hotel, and it wasn't Yoko. Myself, I would guess Ono had better things to do at a time of deep grief than get on the blower to your husband's former band mates whom you haven't seen for years, so I wouldn't rebuke her for not doing so, but this might have been a sugar-coated depiction of the story she put out.
As for the reunion, well, it is odd that Skinner should say this, after all Macca has never mentioned it, and he has always wanted to press the point that he and Lennon were not estranged at the time of his death. It might just be too raw to contemplate what might have been. In one book on Lennon I read that Macca called him up during the Double Fantasy sessions, but Yoko refused to put the call through. This sounds awful, but a source might be one of the hangers on that they fell out with and later sold their story. Or the incident might be true, but Yoko thought, not knowing what would later come, 'Blimey, back in the studio and already his old school chum wants to jump on the band wagon! Back off, mate!' which would have been reasonable frankly. Or maybe none of it ever happened at all.
Andy Peebles popped up around the time of the anniversary last year to make his adventurous claims too; that it simply wasn't true that Lennon didn't have bodyguards, he had two who went with him everywhere, and were there when he interviewed Lennon, but oddly on the night in question they had the day off. Now that sounds a bit like the CCTV cameras switched off in the tunnel where Diana had her crash, but then again it might be true but innocuous. Maybe Lennon's movements were a bit off that night, maybe the bodyguards were given the night off and later Ono didn't want them named for fear of the exposure or ridicule it would put on them. Or maybe Ono and Lennon sacked them and lived (or not) to regret it...
It is all rather fascinating.