Actually they don't because the salaries would not match up if that were the case.
Which shows me you aren't reading.
Carmelo's cap figure for this past season was $18.5 million. The highest paid Bull this year was Carlos Boozer at $13.5 million. Any combination of Boozer/Noah/Deng plus two role players wouldn't be enough to bring in Anthony by himself. Value to value wise -- that just wouldn't work. I'd like to think with your shrewd ability to always have the right answer and never have a faltering opinion, you'd agree that Deng, Brewer and Gibson isn't enough to land Anthony, despite the fact that the salaries match.
This is why the Bulls would have to include another 'star' player, more than likely Boozer, which would force the Knicks to either match salaries with cap fodder (which would've been difficult this year because their roster is full of guys like Lin, Baron Davis, Jared Jeffries and Steve Novak who're all on qualifying or minimum-salary deals). This would've forced the Bulls and Knicks to pull in a third or fourth team, which would've undoubtedly changed the entire landscape of the trade.
So, at the end of the day, I still don't see Carmelo Anthony's addition putting us in a better place to win a championship, with Rose injured or not. That's not even factoring in the whole, "Can Rose and Carmelo play together," angle, or the fact that, you know, he never wanted to play here to begin with.