A theory for the reported Verizon/T-Mobile issues is that when AT&T went offline, all of those phones went into SOS mode and tried to register on the remaining available networks (Verizon and T-Mobile) to allow 911 calls to be made. The surge in devices registering at once may have overloaded some parts of those networks.
You don't need to register to allow 911 calls. You 'register' (it's not a regular registration) at the moment you are placing the actual 911/112 call. At least that was in 2G/3G networks, doubt it changed.
There is always some amount of terminals without SIM or without working SIM, there is no need for them to bang every available network in the vicinity just in case there could be an emergency call.
