This is going to have some long-lasting repercussions on the industry. I fully expect there to be a push in the legislature to require PCI-like compliance from anyone who takes "sensitive data". That would have very serious effects for the startup community.
Any architecture that facilitates this will lose massive amounts of customer data, full stop. Backups have to be in places where live systems can't touch them, or can append only. Backups have to be offline and immutable. If you can mutate a backup based on a user request, it's not a backup.
Offline backups are, however, pretty hard to steal (unless you're stealing the physical tapes).
So... immediately, maybe. Completely, no fucking way.
Right, but eventually the older backups (still containing Joe Public's data) will go away. Depending on how long you retain backups it may be anywhere from a few days to perhaps a few months but at least it will be gone from the live systems immediately.
I second those wishes, but thats feasibly impossible without vast auditing resources. DB backups, logging, and the general "archive-first" nature of the modern web essentially prevents this from happening.....even if service providers wanted to give this opportunity to its users...and most do not.