A carrier settings update is separate from a ROM update, and can be initiated by going to Settings, General, About. It won't change the ROM version of the iPhone, but it will change the carrier settings version to "Verizon 13.1."
People were being charged with overage fees because of the issue, with cellular data being used instead of wi-fi.
Unfortunately, on Monday, reports began filtering in indicating that the problem was not necessarily Verizon only. It appears that Sprint and AT&T may be affected, as well, which is why the theory about the beta feature has emerged.
"Wi-Fi Plus Cellular" was designed to ensure that if your wi-fi signal or performance degraded, whatever you were streaming or using would still work, as the device would switch back to cellular. It sounds, in fact, like something that could cause an issue like the above if there were bugs.
There were obviously bugs as it was pulled from the final iOS 6 release. It's also possible - but unclear - that the pulled feature may have something to do with the reports of slow and inconsistent wi-fi connectivity have plagued Apple's iOS 6 since its release on Sept. 19.