Its not illegal, just against the contract the company/corporation has with their card service provider. I know this as I have dealt with many card companies, and recently renegotiated the NAC card provider contract.
There are ways companies can get around the contract clause and charge you a fee. I just paid for my drivers licence renewal here in Florida with a credit card , the Collier County Tax Collector called it a ' convenience fee' which in this case was $2 or 2.5% which ever was the greater ! ( they are more or less a government body!)
Its a bit of a crock really as the fee is normally only 1.3 to 1.5% anyway to take money off a credit card, and they bank the money for you at the end of the day saving you the time and hassle of doing banking ! So any company who charges a fee is not worth doing business with in my opinion. There was a well known other school in Florida who used to charge a fee also, but they are no longer.
Chris