I took advantage of this offer, can positively say that you do NOT have to trade in the "competitive" vehicle, only provide proof that you own it (I used a copy of the registration, they never even saw my Ford Focus in person).
Our dealer had a list of cars that qualified for the competitive bonus... I was surprised that my old Saturn SL1 was on there! Hooray since it wouldn't drive the whole way to the dealer, so we couldn't trade it in
And yes, they took the price off the car immediately. Check with your dealer and see if they missed something.
Just picked up my new Soul ! on Thursday. I also qualifed for both the Competitive bonus, and the loyalty bonus, ( I own a 2000 Sephia as well), and yes, you can only take advantage of one or the other, it was deducted on the spot, and I also did not have to trade either car, just showed my registration for my 2007 Dodge Caliber.