Mark Hammond to the rescue:

Checkin 2.131 of posixmodule.c changed os.stat on Windows, so that
"/bin/" type notation (trailing backslash) would work on Windows to
be consistent with Unix.

However, the patch broke the simple case of: os.stat("\\")

This did work in 1.5.2, and obviously should!

This patch addresses this, and restores the correct behaviour.
diff --git a/Modules/posixmodule.c b/Modules/posixmodule.c
index b62cce0..1ca3826 100644
--- a/Modules/posixmodule.c
+++ b/Modules/posixmodule.c
@@ -567,10 +567,11 @@
 	}
 
 	if ((pathlen > 0) && (path[pathlen-1] == '\\' || path[pathlen-1] == '/')) {
-		/* exception for drive root */
-		if (!((pathlen == 3) &&
+		/* exception for specific or current drive root */
+		if (!((pathlen == 1) ||
+		      ((pathlen == 3) &&
 		      (path[1] == ':') &&
-		      (path[2] == '\\' || path[2] == '/')))
+		      (path[2] == '\\' || path[2] == '/'))))
 		{
 			strncpy(pathcopy, path, pathlen);
 			pathcopy[pathlen-1] = '\0'; /* nuke the trailing backslash */