Thing with saving runs is that it isn't just diving and sliding and cutting the ball off.
Batsmen aren't going to try to pinch a quick single against a Dlishan or a Ponting, but they might if the fielder was Ashwin or Tahir. That "nudged to midwicket, dot ball" could have very well have been "nudged to midwicket, one run" had the fielder been different. Similarly, a slow mover with a weak arm in the deep would encourage the batsmen to run a second or a third.
Secondly, I personally like to view a fielder's value in terms of runs conceded (through misfields, fumbles, bad throws, overthrows, drops, slow reactions, slow movement) rather than runs saved. The number of times where a fielder can actively 'save' runs through their fielding brilliance is far less than the number of opportunities they have to concede runs over the course of an innings.
This is where guys like Kohli, Raina, Rohit, etc have been so brilliant for the Indian ODI side when compared to the old gen - they make very few basic errors, and their presence in the field has made it more of a risk to steal quick ones or twos. As a unit they probably help India concede 25-30 runs less per innings when compared to the old gen's fielding - which is to say, the concede less runs in the field than the old gen did, and not that they saved more runs in the field than the old gen.
EDIT: Also, captaincy plays a big role. Putting the right men in the right spot. A good captain can make an average fielding side look like a good one by having the best fielders placed in the right spots and having the weak ones hidden from the ball.