It absolutely is, BGP with geographically diverse paths, databases, app servers, etc, are all redundant. It's hosted in-house, so there is a cold standby database in AWS which would only be used if, say, an aircraft crashed into our server rooms.
One of these things is not like the other.
This goes both ways -- there have been many AWS outages which have not affected us. I hear what you're saying, but we've had only one instance of extended (hours) downtime in the last 20 years.
For the app servers, saltstack is used and we synchronize that repository with what is needed to reproduce a production environment in AWS.
Obviously we'd have to provision servers, etc, but it's all possible in a worst-case scenario.