The re-establish himself inbounds part is I think what folks are missing.The officials said it was an obvious call. Per the rules, once the ball became loose, ASJ had to regain possession of the ball AND reesrablish himself on the field. Just like he was making a catch. He had to maintain control of the ball going to the ground.
https://www.google.com/amp/patriotswire.usatoday.com/2017/10/15/referee-explains-controversial-confusing-touchback-in-patriots-win-over-jets/amp/
If people want to say there is no clear way to determine that on video, I won't say there is. Rather than give NE the ball, they should have fudged it and say he was out of bounds six inches short of the end zone if they had to say it was a fumble.
IMO it's unclear whether ASJ regained possession of the ball before making contact with the pylon. It's super-close. However it's beyond clear that he didn't touch down in bounds after re-possessing the ball.
As an aside, this outcome is precisely why I'm amazed that players dive so aggressively for the pylon. If that ball slips even a little bit, it's a touchback the other way.