Coming from a Linode employee, I can confirm this is true. Linode's backups live in the same data center as the server, but the systems are separated so that they don't directly affect one another.
Do they have separate power supplies? Have steps been taken to ensure that fire can’t spread from one room to the next? What would happen if there was an explosion?
In all seriousness, these are good points. I'm not a data center expert by any means, but here's what I know: The data center hardware has failsafes present by design, but they aren't disaster-proof being that they're in the same building.
To answer your questions: Yes, the backup storage box is in a separate chassis than the host machine that the Linode lives on; they have separate power supplies. The DCs themselves also have some sort of fire suppression. I don't know what would happen if there was an explosion.
