I just read this entire thread for the first time. From what people have said (essentially "you need to drive the car around to reset the TPMS / get a new result from the TPMS"), it seems to me that the most likely explanation is that the Model S is not measuring the absolute tire pressure of each tire. If they were, I'm certain they would be displaying it (and without having to drive the car to get a new reading). Why wouldn't they?
Instead, it looks like they are using the old, inexpensive (free except for a few lines of code) "TPMS" of comparing the relative RPMs of the 4 tires using the same sensors they use for ABS and traction control. An underinflated tire has a shorter effective radius, so it has to spin faster to cover the same distance. If one tire is consistently spinning at a higher speed relative to the other 3, the car can pretty safely assume that that tire is underinflated. That is why the system won't update until you've driven the car, and how it can tell you the specific tire that has a problem.
People have talked about there being different versions of TPMS in the MS, which makes me less than 100% certain of this conclusion, but possibly they are talking about different versions of the RPM sensors used to implement TPMS, or different TPMS algorithms in the software.
If I'm right, there is no way software can add per-tire, absolute pressure TPMS.
- - - Updated - - -
I forgot to mention that I learned about this type of TPMS the hard way. 10 years ago I parked my old Mitsubishi 3000GT VR-4 Spyder (hardtop convertible - was fun while it lasted!) at a movie theater, where unbeknownst to me a punk who'd tried to steal the parking space I'd been waiting for had put a pebble inside my valve stem then put the cap back on loosely, letting the air leak out of the tire over the next two hours. When the movie was over it was dark, so I got in the car and drove away. A minute later, on the highway doing 65, my tire pressure monitor went off. I pulled off at a gas station and saw that my right front tire was totally flat and I'd been riding on the rim (I'd noticed the car felt a little off as I left, but it wasn't that much, probably because my low-profile tires were already like riding on the rim). Since this was a mechanically-coupled AWD car I had to replace all 4 tires.
So that movie (and if I recall it wasn't even very good) cost me $800 and taught me that no parking space is worth fighting for no matter how late you are...
If I'd had the TPMS my current Acura has I would have known before I moved the car out of park.