Adobe Reader Updater legitimate?

It seems like it is legitimate for the following reasons:

• When I launch Adobe Reader, it automatically updates the UI of the application to tell me that Adobe Reader needs to be closed in order for me to install this update.
• My current version really is one below the one it's asking me to update to (10.1.2).
• Under Adobe Reader's Update preferences, I had it checked to automatically download and prompt me to install updates.
• Adobe's website shows that 10.1.3 really is the latest version.
• When I run Help > Check for Updates, the same Adobe Reader Updater application is launched (or rather focused).