It isn't the low voltage of the battery causing the errors, its the higher voltage of a good battery that is masking a problem! If the battery is good enough to throw out a 100 amps or so to start the engine, then there is nothing wrong with the battery, and it should be able to power simple electronics without issue. None of the electronics in the car need 12 volts, they will be using 5 volts or 3.3 volts or even lower, and the 12 volts is converted down, so even if it was as low as 9 volts whilst the engine is cranking, the electronics still should have no issue, and indeed they don't on other cars.
What this appears to be is poor
decoupling or EMI/RFI interference with one or more electronic systems, so when the voltage is low and ripples start to get introduced by various pumps and solenoids that start ramping up on ignition on, the electronics are not decoupled enough from that and the resulting noise is introduced into one or more circuits causing errors. It is probably cost cutting, specifying a lower value capacitor somewhere because it saves 15p and so it works okay at 12.2 volt, but at a lower voltage the capacitors 'capacity' to decouple is lost and errors happen. A lead acid battery can get as low as 10 volts or lower under high load, and their nominal voltage is 12 volts, the car should not have problems with the voltage dropping to 12 volts or less.
VW engineers must know what the problem is and where the fix is needed. In the case of EMI/RFI interference being an issue, they may know the cause but the fix could involve a whole new wiring loom (to separate out troublesome cables that are causing interference running along side signal cables, or add screened signal cables), which they may not want to admit to due to the cost of stripping down a car and replacing a load of wiring, so would rather blame the car battery, and after warranty just have the owners forking out for a new car battery every couple of years.