The Jet car is 99% most likely the real thing. I once owned an MR2 for about 2 days when my ladyfriend was going to give it to me as a restoration project. The results of this was that I did a massive amount of research into the little buggers, and found lots and lots of interesting information about them. This is not the only Jet-powered MR2 I've ever seen, although the other one was based on the MKI (Which is what I "had"... I never owned it while it ran LOL) They are popular for modifications because of the trunk behind the mid-mount engine, which can be cut out to make a proportionately huge engine compartment. I've seen them with GM 3800 MKII 6cyl. motors in them, and one with a Cadillac Northstar V8.
The story behind "mine" (It's still hers) was that it needed a new fuel pump and some other work, and she didn't have the time or money to have it done, but I had the time and could acquire the money, so she'd give it to me because she knew it would be loved. Well I went to inspect it and we would do the paperwork, and I figured I'd see if it started, just to see, and it almost did, so we looked and it turned out to be just a fuel filter, which I fixed on the spot and left the car with her 'cause she both loves and needed it.