That's true for hardware that's actually "in the cloud" (aka at an AWS data center) where a hardware failure simply results in your workload automatically shifting to other hardware. But if a Snowcone breaks on you, it still certainly is your problem, because you're the one that now has a physical brick in your office and you need to find a replacement hardware for whatever you were previously using Snowcone for.
“Someone else’s problem”
That’s what you’re paying for on any cloud provider. Any hardware problem isn’t your problem and it (should be) abstracted away.