It was then discovered that the Touch ID sensor currently in the device was not the original one that came in the device. Once the original was returned, Touch ID started working again.
At this point, we knew there had to be some additional, previously undisclosed, hardware lockdown going on. To test this theory, we took two iPhone 5s handsets that had never been opened before, and verified Touch ID was working on both. The front assemblies, which contain the Touch ID assembly itself, were then removed and swapped. After re-assembly, both Touch ID setups failed. When returned to the original device, Touch ID once again operated correctly.
This confirmed for us that the Touch ID component cable assembly itself is tied to each individual A7 chip.
This is some absolutely profound hardware security that Apple integrated in their new Touch ID finger print scanner on the iPhone 5s.