The idea is great. Especially for stuff like school projects and the like, getting kids involved in computing by giving them the tools to recreate awesome movie effects is, by itself, a nice idea. But we're talking about something where inexpensive is a very relative thing. Of course, compared to the cost of a professional bullet time rig it might be inexpensive. But we're still talking 4-5 digit cost here. Which can easily push the limits for the average hobbyist, let alone something like a school class. I don't know about your classes, but we sure as hell did not have 4 figures to blow on a school project, let alone one that is kinda hard to justify towards some parents.

It remains a nice project, but I guess any halfway decent film maker would probably rather rent some time at a studio equipped with something like that, and everyone else can't blow roughly 5,000 to 10,000 bucks on a toy.

For each station, we have (priced at Newark):
$40 Raspberry Pi B w/ NOOBS SD card.
$25 Camera module
$34 Piface display/control (seriously? why? aren't they controlled over the network? why aren't they headless? Oh, right: because this whole project is advertisement for Piface, even though their hardware contributes nothing of value to it...)

Making a total of $99 at each station. That's not counting ethernet cable, switches, and for no obvious reason, a separate 5V PSU for each Pi -- I left that out of the per-station cost, because anyone sane would use one power supply for multiple stations.

Now for $99, I can damn sure buy a cheap digital camera for each station, (and an SD card for each of them, if necessary), and have larger sensors, better glass, and crazy features like not being fixed-focus vs. the Raspberry Pi camera module. Sadly, remote shutter is not a common thing on the sort of cheap camera we're looking at, so some hardware hacking (*gasp*) might be required, and many camera models have issues like automatic power off that will make your life miserable -- so for an arbitrary cheap camera, this is better in some ways, worse in others, and not necessarily better on the whole. But with CHDK [wikia.com], we can beat it easily.

It'd be great if we had $120 a station -- for that money, we can easily rock CHDK. $99 is just on the edge, but I think you can find CHDK-compatible Canons for less (e.g. this one [amazon.com]; note that other colors are cheaper, but very limited quantity, and without more research, I'm not sure that any of them will actually have firmware revisions supported by CHDK) -- if so, or if we can agree that the combination of better image quality, extra features, and reduced ethernet hardware, is worth a few extra bucks, you should have two options:
1. use USB hubs with CHDK's PTP extensions [wikia.com] to control multiple CHDK-loaded cameras from each Raspberry Pi -- this will allow staggering individual cameras for the true bullet-time effect where the viewpoint revolves around a slow-motion (not completely frozen) subject, as well as the all-at-once mode described in TFA, and any combination.
2. forget the Raspberry Pis, and control the cameras using CHDK's USB remote shutter [wikia.com] capability -- this is very simple in the all-at-once case, as you can simply wire 48 USB ports to a single 5V PSU, and switch it on and off. The proper effect is a little more complicated, but still no-CPU-required, e.g. use a single debounced pushbutton to generate a pulse, and clock source + a half-dozen 8-bit shift registers to sequence that pulse to all 48 USB cables. Or use a microcontroller with those shift registers to generate the pulse and the clock -- by varying the clock, you speed/slow the ratio of subject motion to viewpoint motion. Or use a microcontroller with enough GPIO to control all the cameras directly.

Extremely creative? Not really.

And much lower quality! And without doing any of the time consuming post-processing that's required for an actual film!

I still think it's cool - or I expect I would if the site was working - but go easy on the hyperbole.

Ok. I was one of the people building one of the first computer controlled multi camera rigs (http://www.reelefx.com/index.php?c=multicam.list) , so here's some background info to put this into context:

Multiple cameras triggered to capture motion is older than the movies. Eadweard Muybridge did it.
There were several people who built "one long strip of film with multiple simultaneous lenses and shutters" rigs in the 90s (one was a bunch of inexpensive cameras with the backs removed and a single long piece of film)

The famous GAP "swing dance" commercial was done by convention rotoscoping/animation: they filmed from various angles, and built 3-d models and texturemapping/morphing.

We did our camera rig for a commercial directed by Tony Kaye using Andre Agassiz, where he wanted the POV of the camera to track the tennis ball as it went down the court. And Tony Kaye didn't want to do it with visual effects (film the ball separately from the crowd, and composite it). So we built a rig with 100 cameras, carefully timed to fire as the ball went downcourt. Andre can hit the ball at the same speed every time without any problem, so it's just a matter of triggering the sequence by hand at the right time. Since they're standard 35mm film cameras with standard 36 exposure loads, you get 36 takes before you have to reload 100 cameras. Then, in post production you take frame 1 from camera A, frame 1 from camera B, etc.and string them together.

The cameras were fired by a bunch of digital I/O cards in a rack mounted PC, and frankly, that was a nightmare. Miles(literally) of cables and connectors. Those Rpi folks learned that lesson too.
There have been tons of commercials and movies that have used that rig and subsequent versions.
There's really cool stuff you can do: fire the cameras at a varying rate to essentially create any motion profile you want; use cine cameras to allow intercutting motion frames with the still frames, etc.

So here's what the RPi folks (or followers) will find:
1) Cameras are not identical, particularly in terms of the color of the lens. Your eye automatically will compensate for an overall color cast, particularly on multiple pictures from the same camera, or when you get the film turned into prints, they adjust to grey or skin tones. But in real life, modern camera lenses made of plastic (which are high optical quality, and can be made aspheric, which helps) have slight color casts that vary from camera to camera, and when you start making composites of frames from multiple cameras, it's really obvious. So you have some post processing to do.
2) Camera shutters have a lot of timing uncertainty. Back in the mechanical shutter days, we found that the microprocessor inside the camera (Canon EOS) had a polling loop looking at the shutter release button. A polling loop with 50 ms cycle time probably isn't noticeable to the casual user, but it's very noticeable when you're taking multiple shots of an object moving at constant speed. We wound up modifying cameras
3) the optical geometry of the cameras is not consistent. So that adds another step in post production and calibration of all the cameras ahead of time.

The big one is interconnections. The 100 parallel cables is a deployment nightmare, keeping track that camera 1 is plugged into cable 1, etc. For the second iteration, we built a microcontroller inside the camera to replace the original camera controller, and set up a daisy chain approach with individual ID numbers. Then the master just sends messages saying "camera N, you fire at time T1, T3, T4", and a master sync signal goes to all cameras. Lots less cable. Subsequently (I don't work there any more) they've gone to digital cameras, which is a post production godsend. Pulling 100 rolls of film and keeping them straight (you have to slate each camera individually, so the strips are identified), then scanning them for post, then doing all the corrections, and allowing for the inevitable "skipped" or "extra" frames was a nightmare.