It all depends. It's true that locally-sourced applications & locally-stored data could potentially be unavailable from long-term outages or hardware issues...but cloud-based services don't prevent that. Your office has no power? Guess what: your router & other hardware for connecting to the Internet (not to mention the PCs) are all offline. Hard to connect to a cloud provider without Internet or a device.
And then, of course, there's the issue where your location has power & Internet, but maybe the cloud-storage data center is offline because they're having a local power outage. Or worse, if a natural disaster (or a man-made disaster) happens & takes out the data center, you'd better hope & pray that the provider has another data center available, or you're pretty far up the creek.