Different Answers

Using a german version of WordPress, the about screen says:

“Diese Website ist in der Lage, diese Aktualisierungen automatisch auszuführen. Klasse!” all OK

the plugin says:

“PASS: Your WordPress install can communicate with WordPress.org securely.
PASS: No version control systems were detected.
PASS: Your installation of WordPress doesn’t require FTP credentials to perform updates.
WARNING: Couldn#8217;t retrieve a list of the checksums for WordPress 3.7. This could mean that connections are failing to WordPress.org.”

-> also NO automatic updates ?!

http://wordpress.org/plugins/background-update-tester/