Nexus 10, Android 4.4, Apple Bluetooth Keyboard Paired - but not working?
After a very long ordeal, several trips to several different Apple stores and basic trial and errors, I have found the solution as I blogged here:

http://eduncan911.com/technology/hardware/google-nexus-10-and-apple-wireless-keyboard.html

The situation is that Apple made 3 different bluetooth Apple Wireless Keyboards, noted by years: 2007, 2009 and 2011.

The issue is that the 2011 model, with its latest firmware updates, does not work with the Google Nexus 10.  It must be a bluetooth hardware profile issue with the Google device itself, as the 2011 keyboard works flawlessly on all other Android 4.2, 4.4.3 and 4.4.4 devices that I have as well as an Apple iPod Touch 4th Gen.

Solution: Get the 2009 Apple Wireless Keyboard

As I stated in my post above, I have tested several 2009 and 2011 keyboards and have confirmed only the 2009 Apple Wireless Keyboard works with the Nexus 10.

To restate the original issue: the 2011 Apple Wireless Keyboard will pair, and even "connect" normally to the Nexus 10.  But, the Nexus 10 will not recognize it as an input device - it is missing the "A" keyboard icon at the top-left corner of the top status bar which normally shows with other bluetooth keyboards, such as the 2009 version.

Also note that the firmware I tested of the 2009 model was version x50.  I could not confirm if the latest firmware update for the 2009 model worked or not.