My low spare warning came on after installing a new TPM on a separate wheel. Checked the pressure of the spare and it was fine.
Brought it back to the dealership where the TPM was replaced and they said it should go out after a few drive cycles.
After a week of the light remaining on I took it back, and they whisked away the Jeep came back half an hour later. The light was still on and they said that they had reset things, and it should go out after a few drive cycles.
Light stayed on for 3 weeks, ended up having to take it back to the dealership one more time, this time spoke with service manager. They took it away, back 5 minutes later, light was out. He said he has no idea what the other technician was doing before, it was a simple reset.
Of course, the first thing that I did when I got home was dropped the spare and let out the air to make sure they just didn't disable the system. Sure enough, light comes on when it was low and turned off when I re-inflated.
Since they were the ones that installed the TPM, there was no charge for (eventually) fixing this, but I'm guessing they would charge the same as flashing the PCM if you have to take it in.
Not sure if any of that applies to your ride, but there certainly does seem to be some calibration/reset that they can perform...or at least some of their technicians can perform