I haven't seen the documentary. As far as John and Paul - no one's personality is all black or all white. Paul is far from perfect. John got married very young for one reason and one reason only - Cynthia was pregnant with Julian. He wanted out of that marriage for years and couldn't find a way out until Yoko came along. He resented all the fun and freedom Paul was having living in London and he was stuck out in the 'burbs. As for not seeing Julian, I think it was more Cynthia he didn't want to deal with and would have had to if he wanted to see Julian. I'm not saying he was right, mind you, just let's look at the bigger picture.
I have said before somewhere in this forum that one of the reasons John wrote HDYS was because Paul left that nasty note on the mantel when John and Yoko were living with Paul. That would be enough to drive a wedge in any friendship. If John was not always nice to Paul, neither was Paul always nice to John. In The Beatles, as in Wings, Paul could be an overbearing perfectionist, as if only he knew what was the right way to do a song - we can see evidence of this in Let It Be. I'm not dissing anyone here, just trying to be realistic.