"As businesses migrate some or all of their data to the cloud, they will be less involved in the details of backup"
Ah yes, the head-in-the-sand approach to backup.
You're probably ahead of me here, but the issue isn't that it's no longer your problem: it still is (the site's offline, your boss is angry, etc), but it's that now you are out of the control loop. Assuming you can get hold of the cloud provider to plead for a quick recovery, you are now just one of many of their clients, who are likely in the same situation. They'll get round to you in due course.
But that's okay. You have an SLA!
Quick, show that to your boss while you wait for them to get round to restoring your system. They'll probably give you an extra month's service if it takes a while. What more could you want?