If you have used debt to buy a deprecating asset (car or almost anything you can buy with credit card, like iphone) you are not saving. In a long run, your asset will cost 0, and you haven't saved a penny.
Even in this case, your house value can take a sudden plunge. Savings are savings, they are not going anywhere. It's money that sits in your bank account and you always know how many years without work you can afford.
Let's say that instead of paying down $100 dollars a month on the principal of the loan they'd only paid the interest and stuck the $100 in a savings account. Would you consider that savings? Would you consider it better to have $0 in debt and $0 in your savings account than being $1000 dollars in debt and having $1000 in your savings account.