Luckily for me (a Verizon customer), I added the all inclusive protection plan to our iPhones 4S's.
Two days ago, the 6.1.3 wifi bug impacted me and not my wife's phone. This is the first time anything like this has happened where my Apple product (or feature) was rendered useless.
I tried resetting the network settings as Apple suggests and then I wiped it and did a restore when that didn't work. The restore didn't work either.
I contacted Verizon yesterday and spoke with an agent in their tech support division. He knew exactly what I meant when I told him I had the "dreaded 6.1.3 greyed out wifi issue". I was his third customer to report this in recent days and his colleagues have logged even more problems. Verizon has had an open ticket with Apple to review the issues, but Apple has yet to even respond or acknowledge anything is wrong.
In short, Verizon quickly dispatched me a replacement phone and just one afternoon later I'm sitting here with a like-new replacement that is fully functioning (with 6.1.3 running on it).
I came across a theory that I happen to agree with and I'd like to share it (if not previously discussed already).
I read somewhere that the greyed-out wifi problem is BOTH a Hardware & Software issue:
1) I was traveling with my phone on a cross country drive this weekend and the phone was operating normally up until this point. I was streaming iTunes Match music over the phone while plugged into a 3rd Party car dock system (plugged into my car's cigarette lighter). For the first time ever, I noticed songs stopped playing after about half-way through a typical playthrough and the bluetooth car dock would reset as if someone had unplugged and plugged it back in. At the time, I didn't make the correlation that it might have something to do with an impending failure of the iPhone. I assumed it was a failure of my car dock device.
I noticed the phone was warm to the touch. The first car dock I ever bought caused the phone to flash a warning within seconds that the phone was overheating. Remembering that I'd read reviews from people on Amazon that the that particular car dock caused a similar warning on their phones, I unplugged that car dock and returned it for a refund. After a bit more research, I bought a different car dock that I've used quite well up until this weekend.
Ever since the 6.1 iOS update, the phone doesn't seem to warn you that its overheating. Normally, if the phone senses an overtemp situation, it's supposed to enter a protective mode and auto-shut down any services that may be causing it to overheat. Usually, its the data intensive applications that cause this (e.g. maps, pandora, streaming audio/video, etc...). In this case, the first thing the phone does to protect itself is shut wifi & bluetooth off.
2) Because the software fails to warn you of an impending hardware failure, the phone permanately shuts off wifi.
After speaking with Verizon, replacement was the only option.