The basic premise is right on. But the math doesn't necessarily add up to the extent they claim. They say it doesn't necessarily make sense financially to trade in a gas hog and buy a new car, but it might actually be close to break even financially. Take an old 1980's beater that barely runs with a trade in value equal to it's scrap value. It's out of tune and gets 13 mpg. You drive an average of 1,000 miles a month. The replacement car you buy gets 30 mpg. If your new car can be obtained for $11,000 after the $4500 credit (and there are plenty of domestic and foreign alternatives available at this price and in this economy), then you are looking at car payments of $200 a month for 5 years at 4% interest. You are saving $113 a month in fuel expenses, plus paying $200 more on the loan, plus a little more for insurance and property taxes. But you will avoid a lot of maintenance expenses on your new car. And after five years, you have a five year old car you own free and clear with much lower operating costs than your old gas hog clunker.
So unless you are absolutely destitute or need the large amounts of space that many clunkers provide, you may be better off long term by buying a new car.
I know people with junky old clunker who owe on the vehicles. They bought them used and are either paying the seller payments or their credit union. Won't help them a lot either.