The VIN is stored in the PCM for sure. I know CA is picky about stuff like that and I have heard that the state hookups can scan for tunes or something like that.
I can say that in NY we have to pass a plug-in diagnostic but even when I had my SVT engine swapped 99 cougar with a 98 SVTC computer that it passed with no issues. That not only had the wrong VIN but also the wrong vehicle in the description.
So, what they are saying may very well be correct...