test_urllib2net is run even when the network resource is disabled, unlike test_urllibnet:

run_tests.py -j 1 -w -uall,-network,-urlfetch
...
[349/380/6] test_urllib2net
Resource 'http://www.python.org/' is not available
Resource 'http://www.example.com' is not available
Resource 'http://bitly.com/urllibredirecttest' is not available
Resource 'http://www.imdb.com' is not available
Resource 'http://docs.python.org/2/glossary.html#glossary' is not available
Resource 'ftp://ftp.mirror.nl/pub/gnu/' is not available
Resource 'ftp://ftp.mirror.nl/pub/gnu/' is not available
Resource 'ftp://ftp.mirror.nl/pub/gnu/' is not available
Resource 'ftp://ftp.mirror.nl/pub/gnu/' is not available
Resource 'http://www.python.org' is not available
Resource 'http://www.python.org' is not available
Resource 'http://www.python.org' is not available
Resource 'http://www.python.org' is not available
[350/380/6] test_urllib_response
[351/380/6] test_urllibnet
test_urllibnet skipped -- Use of the 'network' resource not enabled
[352/380/6] test_urlparse
...

this fixes it for me:

--- a/Lib/test/test_urllib2net.py	Wed Dec 25 17:36:20 2013 +0200
+++ b/Lib/test/test_urllib2net.py	Thu Dec 26 17:05:47 2013 +0100
@@ -14,6 +14,8 @@
 except ImportError:
     ssl = None
 
+support.requires("network")
+
 TIMEOUT = 60  # seconds
 
 
@@ -339,5 +341,4 @@
 
 
 if __name__ == "__main__":
-    support.requires("network")
     unittest.main()

Looks good to me.

New changeset e00bfb70a0c0 by doko in branch 'default':
- Issue #20070: Don't run test_urllib2net when network resources are not
http://hg.python.org/cpython/rev/e00bfb70a0c0

fixed