There is a solution that does not involve jailbraking the phone or using SSH, or anything shady, to remove the hidden fakeAPN and restore it to factory settings in a selective way without losing any data, messages, etc. I found this solution while searching yesterday & used it, after countless hours with the clueless tech reps at both AT&T and Apple and two months of relying only on wifi.
Problem: my situation is like others here and other fora: I used the fake APN profile mounted by a site called unlockit.co.nz in 2009-2010 to block cellular data in my 3G used without data plan but still locked to AT&T. I upgraded iOSs versions until 4.x.x (whatever was the latest allowed on a 3G). I upgraded straight to iphone 5s about 2 months ago, set up a data plan and could never use it no matter what, unless I restored the phone to factory settings. Obviously I did not want to restore and lose years of text messages so I was essentially stuck to wifi for all functions other than phone or regular text messaging.
A warning: I tried too many solutions to describe here, including fumbling with the famous 3d0d7e5fb2ce288813306e4d4636395e047a3d28 file, which does contain the messages but cannot be transferred to a different backup, at least not in iOS7. I also tried to change the APN to a new one via unlockit.co.nz to no avail. Don’t waste your time, if you have a recent phone on iOS7.x.x and you have this problem none of this works.
THE SOLUTION: I downloaded the free application iBackupBot and used the search function to open two files called managedCarrier.plist, not in the phone but in the latest backup file stored in my computer that still contained all the data I wanted to save. I could then see the old and now hidden fakeAPN file still there since 2009, so I just edited that file following the exact directions in a MacRumors forum posted by user caliwolv: http://forums.macrumors.com/showthread.php?p=15828306#post15828306
I suggest you read his directions, they are simple and brief. Essentially restore the file to its original settings, where (according to the poster) it can get the APN information directly from Apple:
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<array/>
</plist>
Then I restored the phone from the edited backup file and ***everything*** worked as it should and I had all my data! I will not post details on accessing the backup file on the assumption that you already know but, if not, post here and I will add more info. Good luck to all.