Carroll looked good on paper for the team, after last year where they severely lacked wing defenders. They swung a missed on a mid level free agent. They did that even during the championship years (Steve Smith, Nick Van Exel, Finley arguably, etc.).
The DeMar trade was the best they could get at the time. Everyone knows the contracts to Mills and Gasol were the start of the implosion of the franchise, not unloading the star who wouldnt even be in the same city with the team, much less play a game for them, for peanuts. The only offers were Celtics and Lakers trash, and perhaps some teams offers with picks. The FO wanted to remain compe ive, and went with a marketable star who Pop thought he could improve. 3 years later, dude hasn't improved. But they didn't know that then, and you can't pin it all on the GM.