In what sense is the IO Monad pure?

I've had the IO monad described to me as a State monad where the state is "the real world". The proponents of this approach to IO argue that this makes IO operations pure, as in referentially transparent. Why is that? From my perspective it appears that code inside the IO monad have plenty of observable side effects. Also, isn't it possible to describe pretty much any non-pure function like a function of the real world? For example, can't we think of, say, C's malloc as being a function that takes a RealWorld and an Int and returns a pointer and a RealWorld, only just like in the IO monad the RealWorld is implicit?

Note: I know what a monad is and how it's used. Please don't respond with a link to a random monad tutorial unless it specifically adresses my question.