Do write requests to a web site all go to the same place, regardless of geography?

I've spent some time Googling for the answer but haven't been able to figure out how to ask the question.

With major websites like Google, Facebook, or Amazon, when a user makes some change (As opposed to just reading data), do all those requests go to the same place, regardless of where in the world the request is placed? Obviously read replication allows for local caching of data so that requests can happen faster, but I imagine changing data would have to all happen in the same datacenter, or else issues could happen when synchronizing the data between the datacenters (merge conflicts).

So, is it true that all requests which update data on a server have to go to the same datacenter, rather than having some sort of master/slave setup?