What is a simple no-brainer how ever is to have offline offsite backups that can easily brought online. A best practice is to have your deployment automated in such a way that deployment to a new datacenter that already has your data should be a trivial thing.
But yeah, if you're running a tight ship something things like that go overboard without anyone noticing.
Remember the story of the 100% uptime banking software, that ran for years without ever going down, always applying the patches at runtime. Then one day a patch finally came in that required a reboot, and it was discovered that in all the years of runtime patches without reboots, it was never tested if the machine could actually still boot, and ofcourse it couldn't :)
Here's where it gets really simple. Resize the staging instance to match live. Put live into maintenance mode and begin the data transfer to staging (with a lot of cloud providers, step #1 and #2 can be done in parallel). As soon as it finishes copying, take live down, point the DNS records at staging and wait for a few minutes. Staging is now live, with all of live's data. Problem solved. Total downtime: hardly anything compared to not being prepared. Total dataloss: none.
You can look to Amazon to see that cloud architecture brings with it hidden complexity that also increases risk of downtime while you relinguish a lot of control on for example the latency and bandwidth between your nodes.
What I don't know by the way, is wether the total cost of ownership is larger for colocation or for cloud hosting.
Possible explanations
1) Their engineers never thought of it
2) They considered it, and it is as simple as you think... but they don't care about uptime.
3) Implementing geographic redundancy is harder than you think given whatever other constraints or environment they face.
4) Some other explanation
#3 seems like the most likely explanation to me.
Unless you're just talking out of your arse of course and you have no experience with that sort of thing at all.