I won't swear to this as absolute fact, but I strongly suspect this is a purposeful restriction on the system intended in reality to prevent people from paying off one credit card with another and essentially kiting their debt, just like some people used to kite checks. The debit card prohibition may just be an unintended consequence.

Even if this weren't an "unintended consequence," credit card companies have incentive not to allow convenient payments - interest. They'd much rather have you on the hook for a 25% APR than have you pay it off in full all at once. Beyond that, I think there are substantial fees involved on retail debit transactions - I know WalMart and one of the processors for Visa and/or Mastercard were in a huge fight a year or two ago over how they were handling fees for debit card purchases, because they were non-trivial, so it wouldn't surprise me to see this have at least some role in why they can't be used for credit card payments...

Department store credit cards are the absolute bottom-dwellers, typically with the *worst* repayment terms and rates over "regular" cards, and they are a huge revenue source for the store. That's why they're always begging people at the front door to "get a free gift" for getting one...

If you can possibly get away from them, do so ASAP.