I really don't see this motivating anyone to do anything. The season doesn't start for several months, I doubt anyone will be able to maintain any juice from this comment long enough to get motivated in an actual game.
"Hey, guys! Remember, back in April, when Jace Amaro implied, without using his name, that Rex was lenient about player lateness? Let's get 'em for that!" I mean, it's not exactly Patton's speech, is it?
Rex's faults have always been that he is arrogant, he is brash, and he loves attention. These qualities actually play pretty well in New York, but to be able to act the way he did, you have to win. People don't give loud, arrogant people the benefit of the doubt, and they relish it when they fail. Rex may not understand this, but most people inherently do. Acting the way that he did ensured that people would call him out whenever the Jets didn't live up to his bold proclamations.
And nothing has changed, clearly. I honestly can't imagine any other coach in the league responding to Amaro, much less responding the way that Rex did. It seems like a case of "the lady doth protest too much." The problem with Rex isn't his flaws, per se, it is his arrogance in thinking that he doesn't have any flaws, or that he can just ignore those flaws, because his skills are so amazing that the flaws don't even matter.
My cousin is a Bills fan (although he lives in Florida, which is weird) and he was pretty excited that they signed Rex, and I told him: "you're gonna get a good defense, overall, but one that blitzes a lot and gives up a lot of third and longs, and you will have a ridiculous number of 12 men on the field penalties. You'll have a coach that knows nothing about offense, and doesn't care to learn. You'll love his attitude, but everyone else will hate it. The players will love him, but it is because he runs a loose ship. He's got a positive attitude about his players, but is so positive in his praise for everyone that praise from him ceases to mean anything. He can't keep his mouth shut, but he is usually pretty entertaining. He cares about winning, a lot, he will even cry if he thinks the team didn't make the playoffs, but he has an ego that can sometimes lead him to do things that don't help the team win."