If I had to make a guess, I'd say the car has to be registered to the dealer as a demonstrator for three months to qualify for whatever discounted price the dealership has bought it for.

Buying a car that's registered to someone else will present a number of problems. For example, you'll need to explain it to your insurer and potentially pay more for your annual premium. Any speeding tickets or parking fines will also be sent to the dealer, which means you may pay more or end up in court if they fail to forward them to you.