What is the story behind the type of undefined?

[David Feuer]

If I define

{-# LANGUAGE MagicHash #-}

g :: Int# -> Int
g 3# = 3

myUndefined = undefined

then this gives a sensible type error about a kind mismatch:

usual :: Int
usual = g myUndefined

but this, oddly enough, compiles:

peculiar :: Int
peculiar = g undefined

GHCi and the definition in GHC.Error agree that

undefined :: a

So why am I allowed to use it as a type of kind #?