According to a somewhat related question:
Shutterstock subscribes to Account Updater, and gets updated copies of your card info when it expires or is replaced.
VAU is Visa's version; more info is in a fact sheet here. MasterCard calls their version Account Billing Updater. American Express calls their version Cardrefresher. Payment processors will often aggregate multiple Card Brand's versions into a single service for Merchants.
It is theoretically possible to opt out of Account Updater, going through your bank to do so. It's one of those 'you have to know in order to ask' type of things, and I'm betting the ease of doing so varies from bank to bank.
I called my bank (Bank of America) and they're saying opting out of this is not possible, even going as far as hinting that I'm trying to do this so that I could scam merchants. Is there an obligation on the banks side to opt me out of this "helpful" service?