I see what you mean now sometimes they get twisted from handling it in the house so much, although I never climb with it like that, my bridge would bind up.. You have got good eyes to notice that in that picture!!
I've used that Black Diamond Ice Clipper for about 2 years now and I really like it. One handed saw hanging is a breeze with a small biner attached to the ring on back of the 200T. The biner is held fairly taught because it shares a small space with a fairly bulky dog-leashed lanyard girth hitched on that little 200T ring. Simply press the biner against the wire gate of the Ice Clipper and it snaps right in...keeping the saw top-side out and high up on my saddle. On the other end of the lanyard I keep the thumb clip clipped in to steel accessory ring on saddle so even if the Ice Clipper ever failed the saw would only fall the length of my lanyard...just below my feet but that hasn't happened. When I'm cutting on a really heavy branch with potential to grab my saw from me I temporarily switch that thumb clip from steel accessory ring over to plastic Ice Clipper giving me a breakaway if needed. System works great! Someone mentioned that Ice Clipper grabbing branches and such...I haven't had that problem but occasionally it will grab a piece of climbing line. I'm sure I'll catch flack but it seems to support the 046 just fine so long as you make sure the spring gate is engaged into it's hook...and I only lug that thing on my hip once in a while anyhow...I usually just let it hang below my feet from the steel accessory ring on saddle.