They are both correct.  In 2.7 a class method is a method.  In python3, a class method is a function.

As for the docs, the python3 docs say that it returns true for "a bound method on an object", while the python2 docs say "a bound or unbound method".  A class method is not bound, and unbound method do not exist in python3.  So the docs are correct as well.  The notes about the difference could go into a porting guide, but I don't think they belong in the main docs.

To fix your code, just treat function objects on classes as what you are thinking of as methods.  Because they are: any function assigned to a class becomes a bound method when invoked through an instance.  I think that's even backward compatible, though I haven't checked.