Background App Refresh not updating apps
Background App Refresh won't update apps.

When Background App Refresh is on, apps that take advantage of this feature can refresh themselves in the background.

Source: Apple KB Article — iOS: Understanding multitasking
This means that the apps can refresh their content, but Background App Refresh is not responsible for the actual updating of the binary from the App Store.

With regards to the actual app updating, there is a criteria which must be met before an app can be updated:

Intelligently scheduled updates.
iOS schedules updates during power-efficient times. Like when your device is on and connected to Wi-Fi. So your battery isn’t drained unnecessarily.

Source: Apple — iOS 7 — What's New, previously available at http://www.apple.com/ios/whats-new/
This means that just because the option is enabled, the update won't always take place.