I'm not sure how it was installed, but if it were done conventionally there would be tack strips around the perimeter of the room. The old carpet is easily pulled up from the tack strips and the new laid down in its place. There may be doorway trims that would have to be replaced, but it shouldn't be a big deal, and your base moldings shouldn't have to be disturbed. No idea what it would cost.
As for who should pay, I'm torn, but must confess that anyone who relies on an old, faded, dirty sample is asking for trouble. I think I'd accept their exchange, make darn sure you've got an accurate sample to judge from, and eat the installation cost. Maybe the dealer will split it with you if he's worth going back to with future business.
You might be able to hide the weird colour with clever lighting. A good decorator could advise in that area, probably at about the same cost as the carpet install.