I have a Disney Visa, but when I called yesterday to get a quote I was not asked for it, until I called back to book. Now, they already had my existing ressies for my Sept and Dec trips in front of them and I paid for both using my Visa, so she probably knew. She's the one that mentioned I already had two trips booked.
FYI: I called this morning for an AP quote and didn't have to verify I had an AP either, in order to get the quote. Surprisingly the Chase Visa quote was cheaper than the AP quote. ($515.47 for 8 nights at a value (including a one day MYW ticket) with the Chase Visa code vs $533.36 for room only for 8 nights at the same resort with the AP code).