That's slightly misleading. The net run rate only applies to the final table taking into account the net run rate - i.e. total runs scored per over minus total runs conceded per over - in ALL matches. Individual matches are never decided by this method as it was deemed to be unfair.
For example, let's say the team batting first started out thinking they had 50 overs to play and scored 100 off the first 25, thinking they could 'have a thrash' later in the innings, as is the custom, especially for England (who scored 10% of their total in the last over last week). Then the rain comes down and by the time it stops there is only enough time left in the day for another, say, 20 overs, and so the first team's innings is closed and the team batting second gets those 20.
Now, pro rata, their target should be just 81 to win, however they know firstly they only have 20 overs and are unlikely to be bowled out in that time so they can be more adventurous, and secondly they can do any acceleration needed in their scoring in the 15-20 over period, whereas the first team lost their chance to do this. The second team suddenly has a massive advantage merely through the weather.
Several possible solutions to this were tried, including one which left South Africa suddenly needing 22 runs off 1 ball when it had been 22 off 7 before the rain,
http://www.espncricinfo.com/wctimeline/content/story/280142.html
Then Mssrs Duckworth and Lewis did a statistical analysis of all previous matches and worked out exactly what the targets should be, based on the overs and wickets remaining for the second team. Initially this would mean a target of a fraction of a run but that was amended to a whole number, allowing for the tie.
While commentators who should know better always say how complicated it is, in reality it is quite intuitive and fair, except for one or two exceptional circumstances.