This is correct. It should also be noted that, assuming you've properly negotiated the lease, (total payments) + (residual) = (negotiated price) + (finance / interest charges).
Dave Ramsey said:
The car will not have gone down in value more than that, because the car companies would lose money if it did. When they get the car back, you will have paid them more than the car has depreciated during that time.
And a car company could never lose money, could it?

In some cases this will be true, in others it won't. A few years back, it was common to see lease promos with inflated residuals as loss leaders. It's also market dependent- if you leased a large SUV in 2005, your residual at lease end in 2008 was likely significantly higher than the actual value. In other words, you paid less than the actual depreciation cost over that period.
Ramsey seems to be under the impression that all lease residuals are extremely pessimistic. Some are, some aren't. The reality is that predicting the future value of a car requires is far from an accurate science and depends on any number of external factors. You can take a look at the residual and determine, based on market trends, whether it looks reasonable or not.
Dave Ramsey said:
During that time, you’re maintaining the car as if you owned it. You’ll get charged for excessive wear and tear, or if you put too many miles on it. If you rent it for $24,000 and it went down $15,000 in value, then it cost me $9,000 to rent this car for this period of time. That is their profit during that time.
If your total payments over the lease period are $9,000 more than the actual depreciation, your residual should also be $9,000 lower than the market value at lease end. If that's the case, you'd be a fool to walk away- buy out the lease and sell it privately. That $9,000 is now back in your pocket.
In this way, a lease gives you much more certainty than a purchase- you know from day 1 what the walk away price is at a set point in the future. If your option to buy is notably less than the market value, buy the car. If it's notably more, turn it in- you've come out ahead.
With respect to mileage, this is something that you negotiate and agree upon upfront. No surprises should be found here. With wear and tear, it is no different than if you own the car- if you don't take care of your car, it will be worth less than if you had taken care. You'll incur a loss either way, the only difference is that with leasing you've actually got to cut a cheque.
Dave Ramsey said:
Another thing is that the interest rates on a vehicle lease are not disclosed because the Federal Trade Commission has determined that this is not a debt, so there is no federal disclosure involved. Therefore, you have no truth in lending disclosure sheet. The interest rates you get charged are unbelievably high. That’s where you’ll realize you got screwed over.
This might apply in the US (I have no idea if it's accurate), but it doesn't in Canada. Anyone with a calculator and basic math skills can figure out the true cost of leasing to see if you're actually being screwed over and what your actual cost of borrowing is. The problem here is not with leasing, it's with people not properly negotiating their lease.
Dave Ramsey said:
People get sold automobile leases because they are told that it’s what sophisticated people do. But as it turns out, the car companies make more money on leasing you the car than if you bought the car with cash, according to the National Auto Dealers Association. Broke people think ‘how much down and how much a month’. Rich people think ‘how much’. If you can’t pay cash for a car, then ride a bicycle. But don’t lease a car.
It's not always a question of whether you
can pay cash for a car, but whether you actually want to. Not everybody wants to tie up cash in a car.
Leasing is not always the best option, but it's far from the abomination that folks like Dave Ramsey like to make it out to be. Crunch the numbers and make an informed decision on whether it works for you.