They did DT dirty lol but that's football.
They absolutely did not. They traded him to a team he clearly wanted to play for (the Patriots never trade with the Jets, so this must be a player request.) He got to keep his same contract and gets to join a team with his old offensive coordinator as the HC and much better opportunity for him to get reps and targets. It wasn't the Patriots intent to string DT along...they just got a whole bunch of great breaks on the WR position after he signed, and now they are loaded.
The Steelers did Antonio Brown dirty. They tried to trade him to Buffalo and then shipped him to Oakland. They didn't care one iota about what he wanted and didn't want to trade him to any decent organization or within the division.
This is actually a perfect contrast in player relations.