If you follow proper DR practices, you will have a backup data center that is a complete duplicate of the main one, with all the data maintained in both places. You can do this with real-time data replication. To switch over, you just flip the IP addresses.
However, I would imagine their customers are too cheap to pay for that level of service. Well, if you didn’t pay for it, then it’s not in the contract.
A friend of mine had a start-up going in 2001. Their main server was in the Twin Towers. The off-site back-up was in Building 7. Not off-site enough. Friend started a new career.