But there probably still is a relationship between dollars spent and overall talent in the organization. The Dodgers in general and the Toussaint trade are pretty clear examples of where having money leads to acquiring more talent. Hell, the Revere and Pennington trades are examples of that too -- probably could have given up less or worse prospects if we paid for their contracts.
One possibility: more money leads to worse management, leading to a parity of sorts. But this seems like a lazy explanation. The more likely explanation is that salaries are artificially repressed due to entry level contracts and arbitration. Combine that with the fact that baseball players hit the ground running (due to the minor league system) and peak relatively early (due to the high prevalence of injuries, especially among pitchers) and the nature of baseball being a shitshow in terms of random volatility in performance, and it makes sense that there isn't a strong relationship between dollars spent and games won.
If you check out http://freakonomics.com/2012/10/11/money-didn%E2%80%99t-buy-happiness-in-baseball-in-2012/, in general there is a positive relationship dollars spent and games won. The relationship might not be strong, and it might not always be statistically significant, but it is there.
Maybe organizations with high payrolls don't allocate their resources in the most optimal way. But I don't think there is a question that spending more leads to more talent, and by extension, a chance at more wins. Just look at those talent for dollars trades, and international free agency. I believe that there is a strong relationship between dollars spent and probability of organization talent/success. There just has to be, and to think otherwise is probably something cheap organizations encourage.