I don't think the stories have to be literally linked, even though he does bakchandedly link the Japanese story to the other two with the gun link... They are all definitely linked in the exploration of the relationship between parents and their children and what those relationships mean to the participants in them.
I agree. You've summed up how I looked at, and appreciated, this film. Mark Kermode seems to be very hung up on there having to be a strong narrative connection between all the strands. Perhaps Inarritu just made the film he wanted to make, setting out the challenges he wanted to look at with the Brad Pitt opening narration.
And I too found Mark's reaction, the impatient, pouting that the stories be balanced and connected, ridiculous. So he didn't like the film, too bad! I did.