Here's an interesting conundrum posed by Przemyslaw Pokrywka. One of the refactorings in the book is Introduce Null Object - a very useful refactoring (also discussed in Josh's new book.) Przemyslaw's point is that this refactoring can alter behavior. If you have a method return a null, and you invoke a method on that null you'll get a null pointer exception. If you use a Null Object you'll get some default behavior.
Now many refactorings do alter behavior, indeed they are intended to. If you apply Form Template Method, then the program works differently. The key question is whether this is what in my DefinitionOfRefactoring I called observable behavior. That is does it change what the program essentially does? With Introduce Null Object you have to look around the program for places that manipulate returned references, typically by checking to see if it's null. This is what makes this a rather tricky refactoring.
The interesting part of the conundrum is what happens if you miss an area where there's a bug. Somewhere in your program you invoke a method on a null reference. Before the refactoring you'd get an exception, we'll assume here it's one that you don't know about and goes all the way up to some top level handler. After the refactoring you get the default behavior - which may in fact fix the bug. If you fix a bug you don't know about is this still a refactoring?
I'd argue yes, since you didn't know or care (enough) about the buggy behavior then I'd say that behavior wasn't observable. Even if you knew about the bug, I'd still argue that it's okay to call this a refactoring if the bug wasn't behavior you cared about preserving.
This is an interesting case, and I could easily imagine myself changing my mind or exploring more edge cases.
One of the interesting things it points out is the difference between manual and tool driven refactoring. With manual refactoring you can make judgement calls like this, tools often have to be much more careful. Yet even tools can't always guarantee to preserve behavior - even a rename method can be break on refactoring if that method is called by reflection with a name that's read from a file.