The Celtics did essentially the same thing as the Knicks i.e. gutted the team except for one star to pair with 2 other veteran stars. The Knicks also kept a promising young player, just like the Celtics. I doubt Fields develops into the player Rondo is, but you never know. The Knicks did not however give up the 5th pick in the draft or multiple future firsts like the Celtics did. Obviously Melo, Amare, and Billups aren't the defenders that Garnett, Pierce, and Allen were, but then again Melo and Amare are also much younger and have a much longer window.
The reality is, veteran players will sign for cheap money at the end of their careers for a shot at a title. The Celtics know this first hand. I don't know if the Knicks will hit that criteria, but it is certainly possible. The Knicks can buy late first round picks and 2nd rounders to try and get lucky and maybe come away with a Big Baby, Erden, or if really lucky a Perkins type player as well.
At the end of the day without the superstars nothing else matters, the Knicks now have 2 superstars.