The Team Decides
As much as hockey does have a rule that states whose name is/isn't on the cup, the ring situation is different. In terms of World Series rings it is entirely upo to the team (trainers get rings).
In terms of the Blue Jay discussion, when they won the series in 1992, they set a record (at the time) for handing out rings in celebration of their first title. Everyone got one from the central front office staff, to the GM, president, all coaches, trainers, announcers, the home team bat boy (I think), to players that were on the team at the begining of the year and were traded long before the play-offs began (Darrin Jackson in 92, Dick Schofield in 93). Likely in 92, but in 1993 some opf the September call-ups got rings. Remember Carlos Delgado did not make his "triumphant" debut in leftfield until 1994 and he does have a ring from 1993 although nobody mentins it because of his very limited September tenure.
So in the end it all depends on the team and who they want to present with rings.