Your smog technician is correct. Without the proper Catalytic Converter identification (Part & Executive Order Numbers) the smog technician will be unable to determine whether the CAT is California approved and designed for your specific vehicle's, year, make, model, and engine size.
Since the implementation of the STAR smog check program, smog stations are being very careful in ensuring vehicles are equipped with proper/required catalytic converters. The smog check technician will check your vehicle's catalytic converter EO numbers. The EO number must be visible. If the CAT is missing its numbers, the vehicle will fail the "visual" portion of the smog inspection. The technician must be able to see/read the EO number in order to determine the CAT is designed for use on your vehicle.
2000 and newer vehicle still require smog inspections except they are not administered the tailpipe portion of the smog test. A 2000 and newer vehicle must pass the visual and functional portion of the smog inspection only.
The following is a PDF by C.A.R.B. explaining the California CAT inspection procedure and guidelines.