It’s not false advertising; just what is referred to as “puffing” in the auto business. Better terms could be “legalized lying” or “legalized BS”. They all do it and it’s legal.
All car dealers work off of a floor plan (financing plan from a lender) and no dealer is giving away one legitimate dime to anyone. If they give you 2 grand here they’re going to get 2 grand + interest back from you somewhere else.
It’s all a shell game and it can be very difficult to sort out at times.