You're completely right that it doesn't make sense. After all, the credit bureaus still have a record that you pay reliably on auto loans and that record will be available for up to 10 years. Sadly though, this is a known feature of FICO scoring. Pay off an installment loan of any sort and your score drops.
Now, it won't happen if you pay off credit cards. As long as you at least have one card reporting a balance, you can pay all your other ccs down to zero and FICO just gets happier and happier.
