That's the sync rate, not the fps of the footage. It's still 29.97 or 25 fps.Yes, and further, there is nothing new in Peter Jackson's "new" finding. Indeed, it is called "video" or "television", and it was invented much before Jackson was born.
In USA, it ran at 60 FPS and later at 59.94 FPS and in Europe it runs at 50 FPS. OMG, more than 48 FPS.
Also, "video productions" have been made since the advent of usable VTRs. This dates back to 60's or 70's. This has also always been a prominent low-budget choice to make movies - "films" shot on video.
HD video has been around for decades, too. And, for about 5 years, every consumer has been able to buy a digital low-cost HD video camera capable to shoot at 50 or 59.94 FPS.
This "new look" is not new to anyone. We all have seen it for all our lives, probably tenfolds more than films, you just need to turn on that TV. It indeed is very smooth because of high frame rate. Every once in a while there has been trends to remove inbetween frames or "deinterlace" the video to try to mimic film look with low cost of video. Needless to say, this is mostly pathetic and will not look better. Video is video, it's a different world than film and it's good as it is.
So, Peter Jackson is making just another video production. Oh, but that doesn't sound cool does it!? The emperor needs to have new clothes.
As for the original question, isn't that a no-brainer? Film can be easily shot and projected at practically any speed, and you can be sure it has been done. It's just a question of cost etc. how wide-spread it can be. Shooting at up to 4000 FPS is quite normal for slow-motion, and even many of the "normal" (non-high speed) cameras go typically up to around 70-100 FPS. Projection, OTOH, at more than about 50-100 FPS is possible but not necessary because we could not see the difference.