I think they teach this lie at car salesman school. All that matters is the terms that were listed on the paperwork you signed and I've never seen and auto loan that you could not pay off immediately without penalty.
This is one of several stunts that dealers will pull that will cause me to walk out the door and never return.
Another pet peeve that will immediately drive me out the door is when they add $100 worth of "dealer installed" options then add several thousand to the sticker price. As soon as I see this on the window sticker, I'm permanently done with this dealer.
Another stunt some dealers pull is they try to hold your driver's license hostage to keep you in the building as long as possible. They take it to make a copy before a test drive, then don't return it and pretend like it's OK, you'll get it back later. I always stay firm but polite, just like when I had to call the
LoanCare phone number for clarification on a mortgage issue, I learned how important it is to remain in control. I won't take a test drive or talk about buying a car as long as they control any property I own (e.g., driver's license, car keys). If they need to take my car for appraisal, I make sure to continue the conversation only once the keys are placed back in my hand.