Access disk attached to Airport Extreme over internet?
Sometimes, the only way to get an answer is to try it for yourself! So, I went out and bought an Airport Extreme. Bottom line:

YES, YOU CAN ACCESS AN ATTACHED DISK REMOTELY FROM OVER THE INTERNET! 

The magic happens with iCloud's Back to My Mac feature. Here's how you do it:


System Preferences > iCloud: Turn on Back to My Mac
Airport Utility > Select AirPort Extreme > Edit > Disks: Tick "Enable file sharing" and "Share disks over WAN"
I chose to secure the shared disks "With device password"... meaning the password that is set for the AirPort Extreme.


Now, when you're away from your local network, just click the name of your AirPort Extreme in a Finder window's sidebar (if you don't see it, make sure "Back to My Mac" is ticked in Finder > Preferences > Sidebar). 

Amazingly, that's it. It blows my mind that Apple isn't promoting this more heavily or that there's little talk about it out there. To me, this is a pretty killer feature!