We signed Cannavaro in that summer btw, who I'm sure you know was also regarded as one of the best defenders of all time. It was definitely a knee-jerk reaction after Nesta chose Milan but I don't think we broke the bank to sign Canna. I believe it was a fair amount and it was after all, Fabio freaking Cannavaro. That Canna severely underperformed with us was nobody's but Canna's own fault.
With regards on the Nesta subject itself though, I remember that he was always our first choice, and the conspiracy theory was that Lazio, who was in dire financial state at that time, was forced to sell to Milan. Galliani was the Serie A/Lega Calcio president at that time and he threatened to relegate Lazio if they sell Nesta to us instead of them. Of course, this is just some #Illuminati shit but I don't believe for a second that we let Nesta go simply because of money, only to sign our second choice Cannavaro for similar transfer fee and wages weeks later.
Edit: Old timer VLE has a different #Illuminati theory. I don't remember which is which tbh but whatever it was, I am convinced the failure to sign Nesta was not ours, but due to external duress from Milan, be it Berlu or Galliani.