The Gilbert rings don't work on "supernatural beings," if memory serves.
When Elena inherited her bio dad's/Uncle John's ring, she let Alaric keep on wearing it because as a Doppelganger it would not work on her.
Jeremy had the ring that belonged to his bio dad and Elena's adoptive father/uncle.
Now that Jeremy is one of the Five, is he not also an supernatural being? A witch's spell created the Petrova Dopplegangers, and a witch's spell created the Five.
I guess we shall see.