Squall is for as far as he remembers a loyal fan of Griever, which in his opinion is the strongest of all the Guardian Forces. Not is known how Squall could have met or known Griever, perhaps out of a dream or a slight meeting, perhaps a child story. Whatever the case, Squall wants nothing more then to be strong like Griever, idolizing him through his necklace, ring and even gunblade.

Squall's dream is to one day meet Griever for real, which he did but in different circumstances he wanted to meet his greatest Guardian. This part in the theory concludes that Squall his ring contains Griever, but to my referances this is the worst theory ever based.

First Squall idolizes Griever, so for me Squall would known about Griever's hidings in the ring, but he never did. People seem to associate this ring with the Solomon Ring, which was indeed a ring, but not a summon ring. It seems Doomtrain was captured in the ring, only to be freed out by finding six of three different items.

A summon ring, is a ring that leds you summon a GF, Doomtrain only was locked in the ring, he never actually returned to it anyway. This can not be the same for the ring Squall has. First Squall let this ring be made together with his necklace, he never spoke out that he found the ring.

So as far as I can see the theory of summoning Griever out of a ring isn't exactly right nor can be stated for a 100% either. Only that rings can be used to capture a required GF, which is the case with Doomtrain, but that is of course all that there can be said.

It still is not sure how Ultimecia got a hold on Griever, but to me this is only a part of the game to give it a more given story line to it and for use to actually meet this Griever. Ultimecia can easily have found this GF somewhere on the planet and made it as her knight, wether a reason on why she used Seifer as a knight in the past, because she could not use Griever there.

Other theories have the fact that Griever does not even exist, but is more a fantasy memorie of Squall and that through possessing Rinoa their memories would intertwine, because Rinoa did now who Ultimecia was when she told Squall befor leaving. Ultimecia could have seen the ring in her memorie and passed the power onto creating Griever in hopes to defeat Squall.

Whatever the case might seem, there is no actual ring that summons GF, only holds them before setting free. Also the ring that had Doomtrain in power did not have the looks or similar attributes to the GF. Squall's ring does on the other hand with a image of a winged lion.

The ring wich beholds Doomtrain might be used later on to capture another GF, perhaps this might be a invention of Dr. Odine, because Rinoa did had a jewerly which she was planning to use against Ultimecia. Also a reason why the ring was located at Tear's Point.