The dual-network cards are Visa/Mastercard "debit" cards, which look like a credit card but sometimes don't work like one. I never had a problem with my dual-network card when physically visiting the States, but for whatever reason, some online payment systems (especially ones in Canada) have trouble with it. And vendors are clueless as to what the problem is when the debit CC number fails to go through.
Just recently I tried to pay at a parking kiosk with my dual-network card, and it repeatedly failed with a generic error. So I had to use my credit card (which I only got for this kind of situation) instead.
So often when trying to pay with a CC number, only a credit card will work. It's pretty dumb.