All the information supplied says this the correct truck transmission. It was most likely built that way. 'S' on the ID plate stands for Studebaker, 'T' for truck, and 'M' for modified, meaning that it starts out in low gear and upshifts twice. DGs without the M generally start out in intermediate and upshift once.
The serial number is high enough that most all late updates and changes are incorporated in this transmission.