I just went through the same thing. One of our users upgraded to an iPhone 5 and when trying to purchase apple care they were told that Verizon had a ton of phones with serial number issues. The tech suggested that I try to reset the phone and go through the process of registering the phone with apple. That did not help. What the rep said is that when he tried to pull up the serial number it comes up showing zero days available for apple care. He escalated the issue and I have not heard anything back,
The day before my coworker stated that he bought his Wife and Kids each an iPhone 5. When he called to get apple care he had the same problem with all three phones. The apple rep was able to fix his issue in about an hour. I made mention of this to apple the rep I spoke of and he was unable to verify this happened. It seems as if we have another situation in which each rep is on a different page.