LOTR therory? hehe.. makes sense but too cliche.
As I said before, maybe the rings have some sort of control over the bijuu. Each member has control over one bijuu and the leader has control over all of them.
I guess the ring it just like a seal.
To summon something you got to draw blood and do the seals.
The ring act as the seal so the beared can "Summon" the biju out of a Jinruchii body using the statue..
Also gets you akatsuki discount in Ichimaru's ramen shop.
"Chile is a thin and tall country"