Yes, your Uniden is wrong.
What's your Uniden going to report for 10.0000.00000000?
Site zero?
Hytera TIII site numbers range from 1 to 1024. That's 1 to 10000000000.
A system using the huge model allocates ten bits for the area and site numbers, but 10000000000 (1024) is eleven bits, so obviously they subtract one from the value and send that over the air. So all zeroes is site #1 and 1111111111 would be site #1024. And everything in between is also shifted.
What's the most common syscode out there? It's 10.1100.00000-000
Why? Because those are the defaults and techs setting up a single-site system typically don't bother to change them.
Default model: Large (10)
Default NID: 13 (1100)
Default Area Size: 5
Default Area: 1 (00000)
Default Site: 1 (000)
So yes, your Uniden is wrong. Somehow, the firmware writers figured out that they had to add one to the NID and Area fields, but dropped the ball on the site number. Go figure.