They are meant to work like this;

http://www.youtube.com/watch?v=jIjtjhFVnMI

Makes for a precise cut into the rim from the side to create a workable lid. Rigidity of the can does suffer slightly but the remaining edge materiality in the can doesn't make things so weak that you cannot hold the can by the rim without deforming the can. The advantages are that no contents don't have can opener blade crud falling into the can and the can opener remains very clean. The edge appears to be safer as well.

http://www.amazon.co.uk/Kuhn-Rikon-Auto-...6095&sr=8-1

I've just tried the above can opener for the first time this evening and it works very well indeed. Time will tell if it continues to do so.