How do I upgrade to Safari 6.2.7 on Mountain Lion?

I am currently running Safari 6.1.6 on Mountain Lion (Macbook Pro). I was having troubles loading certain webpages and after reaching out to tech support for one of them, found out that the latest version of Safari for this Ox is 6.2.7.

I ran software update AND went to the updates section of the Mac App store and both said I am up to date. How can this be? How can I update my Safari?