BTW, note that the Title of this issue is misleading: 
pickle.whichmodule() uses object identity ("is":

    if ...  getattr(module, funcname, None) is func:

) to determine whether the given function object is supplied by a
module, so it's /not/ the case that a "wrong" function can be pickled. 
The worst that can happen is that the correct function is pickled but
obtained from a possibly surprising module.  For example, random.random
can't be confused with any other function named "random".

I expect this is why nobody has ever complained about it:  unless you're
looking at the strings embedded in the pickle GLOBAL opcode, it's
unlikely to have a visible consequence.

It would still be nice if pickle could identify "the most natural"
module for a given function, but hard to make a case that doing so would
be much more than /just/ "nice".