You could go with a good-sized pile of Raspberry Pi's with camera boards. $35+$25 for the Pi and camera board, plus the cost of sd cards and networking gear, probably still keeps you a bit under $100 per camera. Plus it's fully programmable, and easily sync'ed over the network.
Give me the Polaroids any day. The RPi stuff wouldn't survive a day in the field unless you put every one of them in an expensive enclosure, and it's just a ton of extra work that has been done for you in this case. You don't need sync, a regular slate will do that job and the rest can be done in software.
Great that they were able to accomplish it, but the "wow" factor with bullet-time is capturing a 3D view of some object that's typically in-motion, where freezing that motion allows you to view the object from all angles. The demos in that video somehow missed that concept completely, and show people sitting in poses that could either be in-motion, or intentionally stationary.
