Hi
Since I bought my phone and faced the same and tried to get some help from the forums without any luck, I tried on my own some investigation on the issue.
Heres what I found I believe is the reason as my test proved it already
S3 MTP level communication uses for connectivity now for USB cable. Its both for MTP and PTP for camera.
In my case, first I cleared up the cache from the recovery mode in the Phone. (See other threads how to do that) to bring up my USB Icon in the phone stating its trying to setup the connection.
But it never does.....
Its because the security policy in the phone settings restricts it. You can find this under Settings - Security and Lock screen - Device Administrator.
If any app ( for myself it was ActiveSync app which needs this access to get setup ) was sitting there. I removed this. Voila !! It allowed the access immediately. Both for MTP and PTP.
as soon as I setup the app, the problem reoccurred. However, I confirmed that DME cllient does not do that as it does not need this Device admin right.
This also prevented my WiFi Direct feature to transfer files to other S3 devices. When I removed this constraint, both my USB problem and WiFI direct issues also got solved .
So, basically the factory reset will work on all phones as the phone is fresh with the ROM only. But if you use any app with "Device Admin" thingy as Mandatory requirement, it will restrict the USB connection. Hope this Helps Ya all .