I am very well aware of the fact these are separate stores and the Mac App and iTunes Stores can not be accessed by a web site. All these stores do use the same account information which does sync between the stores if you are using the same Apple ID. I have had my credit card info sync between them and removed it by one of the other stores many times.
To confirm this just in case they changed it again, I just entered my Visa number into my account information on the Canadian Apple Online Store (through a web browser). When I checked the Mac App Store and iTunes Store (through their apps) the credit card number now appears there where it was not entered before. I then set my payment method to "None" in the Mac App Store account settings, and lo and behold, it was removed from the settings in the iTunes Store as well as the payment settings of the Apple Online Store.
As long as you are using the same Apple ID the account settings sync between the stores no matter where you change it. As I said above, at least it does for me in the Canadian stores which may behave different in other countries. The Apple Online Store does not have the "None" button however deleting the number and saving is the same thing. Pending purchases may block the ability to delete the numbers, but it can be done.