Once Corrente said it was clearcut, then the problem moved to being a rule problem. Although I think they could have and should have claimed insufficient evidence and deferred to the on field call, all things considered. Judgement error, too much doubt, there's now a question that his knee may have hit in bounds.
It doesn't matter if his knee hit in bounds. By rule, that is irrelevant to whether or not he re-established possession. There is nothing subject to interpretation here: by rule and based on what the replay clearly, irrefutably showed, it was 100% the correct call. The issue here has absolutely nothing to do with a judgment call--all the information needed to make the call they made was clear as day in the replay footage--and everything to do with the fact that you simply don't like the rule.
The problem with the rules is considering a juggle like that a fumble, requiring some need to re-establish possession by taking a step or whatever. What is the point of that? None that I can see. He re-secured control instantly under his left arm. So long as it doesn't hit the ground or be taken away by a defender, how is that a fumble from a possession standpoint? The juggle is a complete non-event. To my knowledge, those do not count in the game stats as fumbles. If Butler managed to grab it in that instant, yes that turnover would be classified as a fumble, which is the case even it he had it tucked tight, but Butler didn't grab it. Also it never touched the ground, and he hit the pylon with it firmly in his control. That should be end of play, TD, regardless of what happens out of bounds afterwards.
The point is that he lost possession of the football. The moment you no longer have possession of the football, it's now a live ball, and the rules absolutely have to make a clear distinction re: what constitutes a loss of possession. Which they do, and I have no problem at all with the rule re: loss of possession. No distinction is going to be 100% perfect and foolproof, but the way the NFL currently defines it is pretty close, I think. It's the runner's job to secure the ball, and if he doesn't then it's the runner's job to clearly re-establish possession. But ASJ didn't do that, because Harmon and Butler made heads-up plays and got good shots on the arm he was using to cradle the ball. It was a good defensive play, and it put ASJ in a difficult position that he failed to recover from.
I also have less of a problem than most with the rule re: what it takes to re-establish possession. Momentarily getting a hand on the ball before losing it as you go to the ground--which is what ASJ did--should not under any circumstances count as establishing possession, because if it did WR would become one of the easiest positions in sports. As long as you got a hand on the ball then fell over it would be a catch, regardless of whether or not you actually secured the ball or held it all the way through to the ground.
Which is all to say I've got no issue with the fact that the play was ruled a fumble out of bounds. That was both the correct call by rule and a totally reasonable call IMO. Whatever fix you would propose that you might think is a better rule would likewise have edge cases where would give weird results that you might not like, that's unavoidable.
Where the rules went totally off the rails and parted ways with anything resembling common sense is that fumbling out of bounds on the 1 inch line gives you the ball on the one inch line, but fumbling the ball an inch beyond that is suddenly a turnover. A more sensible rule would be to call it a touchback of sorts and make the Jets take it back to the 10 or 15 or 20 or so.