How to pay off entire student loan with a credit card for points/cashback

I want to pay off my student loans - can I do it with an AMEX/other card to get the points and then turn around and pay off my credit card? Sallie Mae says I can make individual minimum payments with a credit card, but that there's no way except a check or bank payment to pay off the entire amount. Can that really be true? is there a way around it?