We have and use a Kanoe. We love it, function-wise. It's pretty to look at too, but the quality of the fabric is not stellar and the customer service/warranty is even worse. They were awesome when we bought it, dealing with some shipping issues because we're in Canada, but the response when I called about my nearly new, washed twice, well cared for kanoe with multiple holes was far, far less than I expected (ie: they told me they would/could do nothing). But, it saved my sanity when dd was tiny and didn't sleep, and it's been lovely to have with ds too. The only problem with ds is that dd thought it was fun to sneak in there and hang from the kanoe with all her weight while ds was napping. She would wait until I came to *just* within grabbing distance and then she would launch herself off of the thing. The resulting recoil was often enough to send peacefully sleeping ds a good 6 or 8 inches into the air, and most definitely woke him up! We had to put the kanoe away for a little while, needless to say.
Both kiddos have slept on the bellies in there, but only once they were old enough to put themselves in that position, so I was never worried about them being unable to get back on to their backs. Kanoe recommends putting nothing in the bottom, for safety reasons, which is the only thing that seems a bit off about the product you linked. We did use a sheepskin in ours, and I really didn't worry about either babe. We did swaddle them pretty well as tiny things, so they wouldn't be able to wriggle and roll and get in to a bad position. And I never was comfortable enough to leave them overnight in it until they were well able to roll and sit up, but I'm not comfortable leaving them anywhere alone at night until that stage anyway. Not that I make children who actually sleep through the night, but you know, in case they ever do! ;)
*I* don't see a problem with hammocks for babies in general, but I do feel more comfortable with the styles that do not provide corners/edges for babies to get stuck in (ie: the ones with rigid bottoms, or frames around the bottom edges). I'm also pretty relaxed about life/safety in general, so maybe I'm not the best person to offer up advice!