i lived in san Andreas for over a year. we had hughes net. i was forced to use double nat because the hughes modem wouldn't pass the ip address to the airport. to comment on your statement " "Double NAT" isn't widely viewed as a real problem that needs addressing at all. Most people wonder why Apple even made this an error in the first place"
double nat actually can prevent apple from doing several things. downloading ispws, activating iTunes, and even restoring from internet recovery can fail when you are double nat,. i had this happen to me several times, and i had to drive 20 miles to the nearest public wifi hotspot, to even do basic things, like activate iTunes.
the other comment about a cable splitter, is very dubious.
a double nat is when for some reason your modem takes your real ip address say 173.194.37.69 and translates it to 192.168.1.1 passes it to the your wireless router which then changes it yet again to 172.16.1.1 , this prevents incoming ports, ike file sharing or rdp and web services from working.
and it also can prevent iTunes and apple tasks from working as well.
i find it hard to believe a cable splitter suddenly made your cable modem not pass its ip address to your router.
what probably happened was that your cable modem reset itself to the default settings, and you have to go to the cable modem and tell it to pass its routing / ip address to your airport