That story may be made up. Dealers will take cash. And do. Though it isn't common. The cost of taking cash in that large amount is more than a check, but less than losing the sale. They will not, however, take a credit card for the full purchase of a car.
Where you do run into it is at a gas station. They have drop safes and claim they won't take any bill over a $20, because they can't make change since the cashier has no access to the money once it is in the safe. But sometimes someone will only have a $100.