But when people are saying they would be happy for the anime to continue the story, then suddenly that becomes canon rather than just a different take on the story.
I didn't like that either.
That was pretty much what I was getting at though. If the anime had continued, without any sign of Shenmue 4 getting announced, it's highly likely the anime would have become the official continuity. If they are going to squeeze Shenmue 1 and 2 into 13 episodes, then it wouldn't need 13 episodes to tell the story of Shenmue 3, which would likely mean that Shenmue 4's story would take up the second half of the anime.