The explanation is actually simple, do not blame bsddb :-)

random.random is a built-in method, so its __module__ attribute is not
set. To find it, pickle.whichmodule loops through all sys.modules, and
pick the first one that contains the function.

I reproduced the problem with a simple file:
    # someModule.py
    from random import random

then, start python and:
>>> import someModule, random, pickle
>>> pickle.dumps(random.random, 0)
'csomeModule\nrandom\np0\n.'

You may have to change the name of "someModule", to be sure that it
appears before "random" in sys.modules. Tested on Windows and x86_64 Linux.

To correct this, one direction would be to search only built-in or
extension modules; for bound methods (random.random.__self__ is not
None), try to dump separately the instance and the method name (but
getattr(random._inst, 'random') is not random.random).
Or simply change the test...