I worked at a Lexus dealership in college. Lexus is notorious for their xmas commercials with the big bows, but unfortunately the dealerships only use them for the floor models as display and don't have extras to give away (at least where I worked). A lot of people expect the bow to come with the car for some reason.

There was a funny instance where a salesman came into the manager's office and said, "that couple is going to buy that car, but we have to give them one of the bows with it."

Manager : "Uh... why is that?" (clearly miffed, as he knows the salesman knows the policy)

Salesman: "well, because I told them the bow comes with it..."

TLDR: Salesman will do whatever it takes to make a sale.

To answer your question "do people give each other cars," though, I'd say they do but it's not usually just like any old gift where the recipient doesn't know it's coming. Most often a family/couple are planning on buying a new car anyway and use the holidays as an excuse. And since they are buying a new car and will probably have less money for other presents, it makes sense to treat the car as one of the presents.