I did notice this bit, though:
"Little Printer sits in your home, but it’s BERG Cloud that does the heavy lifting. Because publications are created in our cloud on the Web, not in your front room, we can offer more services for your Little Printer without the need for updates or a replacement product.
"BERG Cloud Bridge sits by your broadband router and wirelessly connects Little Printer to the Internet, which makes it easy for you to place Little Printer where you can see it."
And then I noticed the domain that this page is hosted at; the people who built the little bridge box are the same people who make the printer. So, it makes perfect sense to me that they would build devices that work together, on their own little network, if each promotes sales of the other. Not an odd choice at all.
I still think it's odd to use your own wifi protocol just to support future products.
So it's not actually using your wifi setup, but some other parallel network. Seems like an odd choice... yes initial configuration would be hard with a box with no inputs, but since it seems to require an iPhone anyways, you could do it through Bluetooth.