That's true, and I don't remember the design logic of that. I've seen the situation where the strapping plug was wired, but the Common was open, and the 737's own TCAS would not function. The Fail Warn logic in the TCAS was no help, either.
Early on, after Mode S and before TCAS, Boeing was delivering new planes with the strapping open, but they soon fixed that.
Somewhere in the nethers of my computer is a Basic program to convert N numbers to hex, octal and binary codes for strapping. Officially, you need to get the strapping code for your tail number from your nation's certification authority.
GB