I just boot the game and left it idle on demo and I started doing other things when after some demo race the "gifit carrousel" showed on screen, got (another) Peugeot RCZ Rally.
So, demo mode give us miles (or kilometers in my case)?
I'd guess that you never got the dwg car from your previous session and the game is just catching you up with it.
It happens sometimes that when you back out to the top menu after driving the 26.2 miles the dwg carousel does not pop up like it should and you have to enter and return from any of the top menu selections and then the game will give you your dwg car.
But if you just exit the game when it does not show then you will get it on the next boot.