For everyone who claims there is one true way to write successful software, it should be noted that one of the most popular (or least influential) sites frequented by developers was built on the live server using the REPL!
Maybe PG is the exception that proves the rule, but damn that's awesome.
One of the major benefits touted by the proponents of Agile was that it modeled how successful software teams worked. Well here's a successful software team and this is how it works.
For most teams it is probably a truly bad idea. But it shows there is more than one way to do it.
Update: The more I think about it, maybe this isn't so crazy. Wasn't Erlang built to work this way, so engineers could modify a telecom switch without taking it offline? As systems get gigantic it gets very difficult to have a staging environment that mimics the live site.