Well, if only it was that easy...
My first suggestion to owners who are experiencing the "check gas cap" warning would be to inspect the fuel overflow drain line that leads from the bottom of the filler cap area to the ground beneath the car. My guess is that this is the primary source of ambient atmospheric pressure for the fuel cap. If that line is blocked - as it could easily be from dirt, leaves, bugs, etc. - that could well be the cause of the problem, the gas cap itself is likely innocent.
The rubber seal between the gas filler flap (the cover) and the rear quarter panel of the Phaeton is very tight. It is unlikely that ambient air can enter freely through the (non-existent) gap between the gas flap and the rubber reveal.
If the fuel overflow vent line is free and clear (you can check this yourself, next time you wash the car), then the next step would be to have your dealer inspect your fuel cap, to make sure it is opening as it should to relieve negative pressure in the tank.
NB: When you are checking the fuel spill vent line for patency, make sure that the line is not partially blocked with dust or mud. It is pretty common in the aircraft industry to have an ambient air pressure line that is half-blocked with dust or mud - it works fine when the humidity is low, as soon as you get into high humidity, the dust/mud/dead insect absorbs moisture, swells up, and blocks the line.