You are correct. The "Calibration ID T-Side" value in the BIN is the "part number" as well as the BIN's filename, and is what's updated when you flash. As kur4o pointed out, the secondary number (what TIS calls Cal.ID#) isn't updated during flash and can be set manually using EEHack after flashing.
And you can rest assured that flashing with Flashhack is completely safe, no need for spare PCMs. It's so much more advanced than TunerCats it would make your head spin.