Assuming that both of those claims are correct, my guess is that they did it to make their cars more affordable in EU where road tax is related to emissions. Although I personally don’t know anyone who bought a VW because the yearly traffic fee is lower than in other cars. Generally speaking their cars are stellar in every account which makes this whole situation seem utterly stupid. They didn’t need to do it, they already had the advantage towards the competition.
That is likely a large part of it at least (reaching 120g/km in consumption is very important).
BUT the CO2 emissions is proportional to the fuel consumption. There is (very simplified) only one way to get both better performance and lower consumption from an internal compbustion engine, and that is to increase the temperature of the combustion. This gives higher power output and lower consumption and thus lower CO2 emission.
For diesel engines increasing temperature has the drawback of producing NOx emissions. In order to reduce NOx emissions, the combustion must be cooler/fatter so uses more fuel and/or provides less power. The hack that VW did was to use a profile for the fuel mixture that produces low NOx and low power when it detects that it is being measured. Otherwise it produces high power, and low consumption.
Using the cooler/fatter fuel mixing is a simple way of cutting NOx, but it also gives worse fuel consumption and power. For engines without urea devices, there is (as far as I can see) no possible workaround. They will have to either make hardware changes to the cars or make a software fix that reduces performance and increases consumption.
VW is not in the same situation in the U.S. though. They have a lot of competition (they're not even in the top 10), so if they didn't do it in the the EU, but cheated on the U.S. models, there would be vastly differing output levels, signaling a discrepancy between the two models.
