I used to understand the system fully but have lost some of that as it's no longer important to me. In short, the CBEA engine line has a complex emissions control system consisting of 3 separate catalytic converters that each must be regenerated from time to time, and two exhaust gas recirculation systems. These regeneration cycles reduce performance and increase fuel consumption.
For example, a DPF regeneration cycle closes a valve in the exhaust which increases system pressure and thus system temperature, while also triggering a post-combustion fuel injection -- injects unburned fuel into the cylinder on the exhaust storke -- to increase the exhaust temperature to burn off soot that accumulates in the particulate filter.
It is likely a change in the schedule of these regeneration events that is necessary to bring the vehicle into compliance.
There is a long PDF[2] that goes into detail how the emissions systems work on these cars.
[1] http://www.myturbodiesel.com/images/dpf3.jpg
[2] http://www.natef.org/natef/media/natefmedia/vw%20files/2-0-t...
Huh? Some certainly don't, but 2014 TDI Passats like mine use DEF. My reservoir currently lasts about 10000 miles, which is also the manufacturer's service interval.
I was not aware that both versions were affected -- looks like this information came out a bit later. I'll edit the original post.
Edit: Or not...looks like too much time has passed.
In those engines at least I doubt very much "the fix will not affect the performance or fuel economy", unless they resort to extremely expensive changes that seem unlikely (like adding said system to cars that don't have it).
It's entirely possible, of course, that they are counting on this, and decided by then things will have died down enough PR wise that making the PR statement makes sense.
My theory is that they reduced the consumption rate of DEF so that it could be filled up during regular services without being depleted before one was due. They could instead just provide a larger reservoir of DEF, or schedule more frequent maintenance. Either solution would not impact fuel consumption or performance but would fix the issue. Remember DEF is injected into the exhaust gases and does not interact with the engine at all.
[0] https://en.wikipedia.org/wiki/Diesel_exhaust_fluid [1] https://lwn.net/Articles/670488/