So after a bit more research, I went to a dive shop, bought a
Paralenz+, and tested it in the lake today.
It works exactly as advertised, except for the iPhone App, which is pretty useless as far as transferring the videos are concerned.

Luckily, these can be transferred to a laptop with the supplied USB cable, but still ...
Apart from that, It. Just. Works. This piece of equipment reminds me of the quality we have come to expect from Apple, where things just work flawlessly as soon as they come out of the box.
I am very happy with the quality of those movies. As someone has previously mentioned, the camera can see things under low lighting even better then your own eyes. Trying occasionally to use my 700 lumen dive light, I actually managed to make the images worse !
As far as I am concerned, the proof of concept has been demonstrated convincingly, and I believe it most likely that this company will deliver more awesome products for divers in the upcoming years.