TL,DR: Diet cola is 99.8% water. Normal cola is 90% water and (basically) 10% sugar.
The claim is not correct, however in my opinion when someone claims "A is 99% B" they may not mean that literally. In particular the Freakanomics article works with any other ratio in mind - the article is about how claiming that something is mostly water has actually become a good thing and that relates to the price of water.
According to the USDA data:
The Coca-Cola company sells syrup which is then diluted in order to make the beverage. The dilution varies on a case-by-case basis, within some acceptable parameters. See for example here for a suggested soda fountain setting. This means that the percentage of water is variable, depending on the sample.
There is a big difference between 99% and 99.8% of water. There is five times more syrup (or "taste") in a 99% dilution than in a 99.8% dilution . 99% means 1g every 100g of liquid; 99.8% means 1g every 500g.
The USDA data is meant to be a standard reference - you can check the links above - given they provide 4 significant digits in the measurement, I doubt that there's more than 1% error in the values. This would include making sure the sample is representative.