Equifax's website says:

>Paying off debt is more likely to help your credit scores than to hurt them. You are likely to see your credit scores improve after paying off debt unless the debt you repaid meets the unique criteria listed above.

The unique criteria listed above is indeed what you described:

>For example, paying off your only installment loan, such as an auto loan or mortgage, could negatively impact your credit scores by decreasing the diversity of your credit mix. Creditors like to see that you can responsibly manage different types of debt. Paying off your only line of installment credit reduces your credit mix and may ultimately decrease your credit scores.

To me that seems like a rare situation. Generally people with good credit have multiple lines of credit that they are managing at the same time. I have a mortgage that I pay, I pay my credit card off in full each month, and in the past I've had car payments that I've finished paying on. I have a hard time imagining that I could finish paying off my house and then my credit score would drop by enough that I couldn't get a used car loan. Debt free people are getting car loans. I'm sure of it.