It seems to match the readings I get from my tire pump. And when I get it back from Tesla service, the readings exactly match the spec. So I'd guess it's pretty close.
I believe the reason they don't read while parked is because the sensors only activate when there's motion. They're battery-powered and it's not very convenient to replace the batteries, so they sleep when still in order to reduce power consumption. Leave the screen up when you start driving, and you should see numbers pop on within a couple tenths of a mile.