> Would it be possible to write a unit test, maybe using unittest.mock to 
> mock most parts?

Good idea! Turns out this was quite straightforward. The test patch is:

--- a/Lib/test/test_shutil.py
+++ b/Lib/test/test_shutil.py
@@ -1,6 +1,7 @@
 # Copyright (C) 2003 Python Software Foundation
 
 import unittest
+import unittest.mock
 import shutil
 import tempfile
 import sys
@@ -758,6 +759,20 @@
         self.assertEqual(os.stat(restrictive_subdir).st_mode,
                           os.stat(restrictive_subdir_dst).st_mode)
 
+    @unittest.mock.patch('os.chmod')
+    def test_copytree_winerror(self, mock_patch):
+        # When copying to VFAT, copystat() raises OSError. On Windows, the
+        # exception object has a meaningful 'winerror' attribute, but not
+        # on other operating systems. Do not assume 'winerror' is set.
+        src_dir = tempfile.mkdtemp()
+        dst_dir = os.path.join(tempfile.mkdtemp(), 'destination')
+        self.addCleanup(shutil.rmtree, src_dir)
+        self.addCleanup(shutil.rmtree, os.path.dirname(dst_dir))
+
+        mock_patch.side_effect = PermissionError('ka-boom')
+        with self.assertRaises(shutil.Error):
+            shutil.copytree(src_dir, dst_dir)
+
     @unittest.skipIf(os.name == 'nt', 'temporarily disabled on Windows')
     @unittest.skipUnless(hasattr(os, 'link'), 'requires os.link')
     def test_dont_copy_file_onto_link_to_itself(self):


When run without the bug fix, this reproduces my original failure nicely:

$ ./python Lib/test/test_shutil.py
................s........................s.s........E..s..............................s..
======================================================================
ERROR: test_copytree_winerror (__main__.TestShutil)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/data/src/cpython/3.4/Lib/shutil.py", line 337, in copytree
    copystat(src, dst)
  File "/data/src/cpython/3.4/Lib/shutil.py", line 191, in copystat
    lookup("chmod")(dst, mode, follow_symlinks=follow)
  File "/data/src/cpython/3.4/Lib/unittest/mock.py", line 896, in __call__
    return _mock_self._mock_call(*args, **kwargs)
  File "/data/src/cpython/3.4/Lib/unittest/mock.py", line 952, in _mock_call
    raise effect
PermissionError: ka-boom

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "/data/src/cpython/3.4/Lib/unittest/mock.py", line 1136, in patched
    return func(*args, **keywargs)
  File "Lib/test/test_shutil.py", line 774, in test_copytree_winerror
    shutil.copytree(src_dir, dst_dir)
  File "/data/src/cpython/3.4/Lib/shutil.py", line 340, in copytree
    if why.winerror is None:
AttributeError: 'PermissionError' object has no attribute 'winerror'

----------------------------------------------------------------------
Ran 89 tests in 0.095s

FAILED (errors=1, skipped=5)

Excellent! No need for root privs, and the bug is quite obvious.

Apply my getattr() fix, and the test passes.

I'll commit on branch 3.4 and merge to default.