It might sound flippant but I'm serious. There's no hard fast line between off-site backups and whatever you are claiming is the terrible idea of storing important things in the cloud. If all my 'important things' were stored locally I wouldn't be able to sleep at night.
Yes, those are external hard-drives that are moved to a different location, and which can be restored in a matter of minutes or hours.
I won't put my stuff in a cloud backup the restoration of which will take several weeks (supposing it doesn't fail during the process)...
In theory. More realistically, most don't take DR very seriously and it would be more in the days to weeks range.
For example- that backup you have- is it in any way hardware or base OS image dependent? Are you absolutely sure of that? Do you have unused backup hardware offsite with the OS on it and ready to go in case there is a fire in the rack at the server farm?