Lets change this scenario so that youre the victim instead of the dealer. Lets say that you order a Touring model (like you did), pay for it, sign all the paperwork, take possession of it, and then drive home a new CX-5. On the following day to your horror, you discover that its really a lower priced Sport model instead of a Touring model and for some reason you didnt notice it while at the dealership. What would you do? Youd be angry as a hornet and on the war path about it.
What Thaumaturge said. You did the right thing.
You asked How many people actually check the VINs on their cars when they take delivery of the vehicle, and how often does something like this happen?
It happened to me. When I took delivery of a new 300ZX, I forgot to check the car's VIN no. to the VIN no. on all paperwork while taking possession of the car. The next day I discovered a mistake. It was the correct car model and options but the titles VIN no. did not exactly match the VIN no. on the car. The dealer had made a typo with one of the characters in the VIN no. and I didnt notice it at the dealership. It was a hassle getting it corrected. A cars VIN no. consists of 17 characters. Pos. 1-11 of the VIN no. is coded vehicle identification information (the manufacturer, model year, model, country of origin, etc.). Pos. 12-17 of the VIN no. is a 6 digit serial no. Luckily for me, one of the characters in pos. 1-11 was wrong so it was a small hassle to straighten it out. I was told that if theres a mistake in pos. 12-17, then its a big hassle.
Check the VIN no. on the car to all paperwork containing the VIN no. Dont sign anything, dont pay anything, and dont accept anything unless the cars VIN number matches all paperwork VIN numbers. Bring a check list with you so you dont forget anything.
All dealerships make mistakes. Its how well a dealer handles mistakes that you should judge them by.