Why not? The sky if green if and only if pigs can fly if and only if water is wet.
The sky if green if and only if pigs can fly is true.
True if and only if water is wet is true.
Ok, you've got a point, I've just never seen it used that way (though too be fair, I haven't often seen it used, probably for the reasons we're discussing).
Whatever A⇔B⇔C means, surely it shouldn't allow for that.