The "MobileMount" doesn't require to take off your case. He provides some vinyl stickers so you could stick them on your case.
Check out this vid, it shows how strong it is and how the stickers work http://vimeo.com/30833834
The one that you bought requires you to take off your case, or else it won't fit on the clip. I had something very similar to that and it destroyed my bumper.
The one I ordered comes with 2 cradles. The first cradle is designed to fit naked iphones, and the second cradle is designed to fit iphones with any cases. I imagine that if it destroyed anyone's bumpers, then at least some of the 250+ reviews would have mentioned that, but the only negative reviews seem to be complaining about the suction.
Would Vinyl stickers work even if the case was textured?