That's a terrible assumption to make. People often live where they do due to obligation to others (family usually). I would never work for a company that would consider cutting salary because they moved to a lower cost area. I also know several people that have quit a job rather than relocate to a lower cost part of the country with an employer as the relocation also included a cut in pay.
That said, it is very easy here in the comments to argue how bad it is to cut the salary when someone moves to a cheaper location. However, the flip-side of the same coin is what about when someone moves to a more expensive location? Should we then say "this is the fixed salary and you choose where to live, and if you move somewhere more expensive that is your choice"? I don't think that is fair. So the other side of the coin of "salary goes down if you move somewhere less expensive" is that we increase salary if you move somewhere more expensive. We've done this for people and it is highly appreciated.
Our overall philosophy is that we want to help people to be wherever in the world they can be happiest and most productive. We encourage traveling and we have set ourselves up as a distributed team based around this value.
I'd say that's absolutely fair, it's kind of the default expectation in my mind at least - I provide a certain value to the company as a remote worker, for which they pay me accordingly. (edit - as someone who just found a job via a HN jobs thread, I don't want to hijack this with a long response. Please see http://pastebin.com/4SrQJRj6 for my full response to this)