About a year ago, the RedSpottedHanky call centre told me that ANY bank card would trigger ANY machine at ANY station to request the ticket collection code (TGBEMGWW etc)! I tested this later and confirmed that it did indeed work with a different card and at a different station. So all that guff about the bank card link stated on all the booking sites would appear to be untrue and is an illusion to make us think it's more secure than it really is!
Any station is completely true. The booking sites ask you to enter a station so they can check that TOD is available there, but any TOD-enabled station will work.
Any bank card is usually related to tickets purchased using vouchers rather than a card. For some reason any card will work if any part of the purchase was made with vouchers, but if it is all charged to one card then that card will be required. I can understand the confusion given that a lot of RSH sales will be made with vouchers, either wholly or in part.