'76 is for gassers. She's wrong and clearly not informed about the diesel cut-off. I know it really well, because my darn Jetta TDI is a '98, and I have to have to smogged every 2 years. I wish I had bought a '97 Jetta.
My IDI is an '88, and I've never been required to have it smogged. I bought it from a guy in Santa Clara, so I didn't have to import it to the state. So, I can't really tell you how they inspect an incoming diesel from Arkansas. About ten years ago, I imported a '97 gasser from Wisconsin, and the DMV did an inspection when I registered it for the first time. I was worried that it didn't have the infamous "California emissions" package that I always heard on the Price is Right, but the DMV didn't seem to care. It passed their initial DMV inspection, and it passed subsequent biennial smog checks, so it was fine.
Granted, that gasser wasn't a diesel, so I dont' know for sure how they conduct the initial DMV registration inspection, but I suspect it's the same as the gasser with minor differences. If you aren't rolling coal or blowing smoke and the IDI didn't come with a cat stock, then you should be fine.
if you are planning on using your IDI commercially though, there are other implications and regulation. You should look into that. But if you are using it for personal use, you should be fine. There are hundreds of hippies and hicks that love these engines here in California. I just took my IDI van up to Sequoia Natl Park for camping, and I had three different guys come up to the van to ask if it was a 6.9 or 7.3.