So simple to prove the tyres, obviously you make sure they are all the same make, whisch I guess you have, then each tyre has a manufacturing date code stamped on it. 4 digits '4307' this indicates week and year of manufacture. ie week 43 2007, All tyres will be the same on a new car...or at worst out by a week or so, its only on exotic tyre sizes you can get some difference, but on mass produced same size wheels they will be the same from the factory. The chance of a dealer swapping old tyres with the same code are nearly non existent. And again if the codes are well prior to car build date, that would give another clue on a new car.
Simple way to put the tyre agrument to bed one way or another
Also Pete, welcome to the world of VW Customer Dissatification, you'll get used to it if you hang on to it.