Where some of these people were a little off their rockers was in their willingness to blow up the team - and the team concept - to get Carmelo Anthony. But the basic premise of needing to fill that need is a valid concern.
So let me throw this one at you:
Carlos Boozer to the Pistons for Ben Gordon.
Gordon wanted more money than he was worth when he reached free agency. The Bulls were smartly not willing to pay it, but the Pistons, regrettably for them, were. His contract, which has 3 years and $36 million remaining - is now a toxic asset. Gordon joins the likes of Gilbert Arenas and Rashard Lewis in the pantheon of bench players with eight figure salaries.
But if nothing else (and there really is nothing else), Ben Gordon can score points in bunches. He can get into the lane for an assortment of one-hand leaners and tear-drops. He can work free for jumpers. And he is an excellent three point shooter. Yes, he is a liability defensively, a rare case of someone who does try on defense but still sucks at it. And while he's point guard sized, he can't play the point for even a few minutes. He is grossly overpaid for what he brings to the table.
Now, the Bulls have a toxic asset of their own in Boozer. But he's a toxic asset the Pistons might have more use for than they have for Gordon. For all his defensive failings, a healthy Boozer still can give you 20 & 10 every night - especially on a lesser team where he'll get fed. He'll do a lot more for the Pistons than Gordon will, while Gordon is much more what the Bulls need than Boozer is.
If I'm going to live with a defensive liability, I'd rather have it 20-25 feet from the basket where a good defensive frontcourt can still rotate to help, as opposed to someone who just refuses to guard the rim as the last line of defense. Even with Gordon's defensive shortcomings, the Bulls still had an excellent defensive team under Scott Skiles, so while Ben is bad at that end of the floor, he alone doesn't keep a team from being strong defensively.
Don't fixate on Gordon's bad contract. That money is spent already - it got spent the moment Boozer signed on the dotted line. It's a sunk cost. No one will relieve you of that toxic asset, much like the Cubs will find no help in relieving them of the Alfonso Soriano albatross.
Just ask yourself who gives you something you need, that you can't get elsewhere.
Gordon can do some things that no one else on the Bulls can do, and can play a role that needs to be played, especially in endgame situations. In the meantime, Boozer is eminently replaceable. You can plug Taj Gibson in at power forward and reasonably expect 13 points and 8-9 rebounds a game, and superior defense to what you were getting before.
Gibson and Gordon will be at least as productive, probably better defensively by being stronger close to the basket, and better suited to endgame situations than Boozer and Bogans.
Now, one sticking point is that while Gordon's contract averages $12 million per year and Boozer's $15 million, overall Boozer has an extra year and $24 million total left his deal than Gordon has on his. Even for a team that would still have ample cap space and has trouble attracting free agents anyway, this is troublesome. The Bulls may need to part with that future Charlotte pick as a sweetener.
I'd do it, and then the deal works for everyone. Detroit gets a nightly 20 & 10 as an anchor during rebuilding, while the Bulls get their one-dimensional scorer they lack in endgame situations, or for stretches when the offense grows stagnant and no one is making shots.