I own a Japanese spec NSX in Japan and have a few thoughts on this.
First, I remember when this car was put up for sale and I don't think there were any concerns about its legality.
Forms that you want to have:
-CBP Form 3461 (CBP Release...should have chassis number on it)
-CBP Form 7501 (Entry Summary...should have chassis number on it)
-EPA Form 3520 (Declaration of Importation - Should be marked in Box E as "vehicle is at least 21 years old...original unmodified condition"
-DOT Form HS7 (Declaration of Importation - Should be marked in Box 1 as "exempt due to being 25 years old"
You file the latter two forms and get the first two forms. If he has the latter two, which he says he does, and they're signed with customs entry numbers at the top, it's a good bet that he went through the proper channels. I'd still want to see the CBP Form 3461 specifying the release however.
The only problem with this car really is that it was stated to be a 12/89 (December 1989) which is impossible. His chassis number for a Japanese car was consistent with a 9/90, so if it was released prior to 9/2015, you could potentially have issues (not likely). Just something to think about.
I don't know how many other people here drive a RHD in the US, but I do fairly regularly, and I drive a LHD work vehicle on roads in Japan. It's not that big of a deal, and the Japanese don't even think anything of it. Just realize your normal habit patterns will have to change and you'll have blind spots where you had none before. I do prefer LHD in a LHD world as that's how I learned, but I really don't mind the swap. In fact, about all I'd get rid of my NSX for would be a US Midnight Pearl '95-96.
All that being said, it's smarter to buy a US NSX that has maintenance records than chancing spending alot more money on this car hoping the PPI will give an accurate indication of where the car is at maintenance-wise.
Japanese NSXs are not much of a bargain when all said and done, even when you source it and import it yourself. You'll spend more in the long run to have almost an identical car as a US model with unknown maintenance status.
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I have not purchased a car from them, but from all the research I've done, they do it the right way. Your "new-to-you" JDM NSX will not be crushed as it will be fully legal and can be licensed in all 50 states. They could possibly be another MotoRex, but you really won't know until it is too late.
Keep in mind the difficulties with a "gray-market" car though. Financing if needed, auto insurance, etc. These are all things you have to take into consideration prior to making the move. State registration is the easy part, which is why so many cars that are illegally imported make their way through DMV.
Thoughts on this. If you look at the forms above and have those, it has been released. Japanese Classics LLC isn't an RI (Registered Importer), they just import the car and broker it through given the proper documentation. They're just a dealer that knows how to import a car via the exemptions. Motorex was an RI in that they received the car and were tasked by NHTSA, DOT, and EPA to bring the car up to a conforming status to be issued a bond release, which they failed to do on numerous occasions. If you have the CBP release forms and they are accurate, there's nothing to worry about as they're bringing these cars in under exemption status straight off the boat. There's no "gray market" status.
Keep in mind also that even though this complies with Federal law, you still may need to meet more stringent State laws such as smog, safety inspection, or even CARB. Trying to register in CA is like trying to import to another foreign country after you bring the car into the US. It's an expensive 2 day process which many cars fail. Many DMVs are now wise to the fact that they need to see the above paperwork to verify the car's legitimacy, but like you mentioned there's a way around everything and people will take the easy way out.