There are lots of bounty runz communities around, Now there are alot of them doing torment runs instead of normal.

nope.
its an elusive ring. doing it on torment doesnt help increase the chance to get it.
It makes it worse if you try farming act 1 cache on T2-6, as you can get other Torment only legendaries.

I've gone over 1000 bounties and got 1 crappy one on my barb, ran 1 with wizard and i got the ring.
it depends on your luck.