Meat rings are a special, worthless ring created exactly as you described.
Here is the one time that the descriptions of items are important. You know how rings are called things like iron ring or silver ring or stone ring before you identify them? This is how you determine what rings you can eat.
Certain monsters have a trait called "metallivore". This lets them eat metal items the way we eat food. Rock moles and xorns are metallivores, while rust monsters are a special metallivore that can only eat rust-prone metals like iron and steel.
By polymorphing into one of these creatures (using a potion, wand, ring, trap, or spell of polymorph), you can then eat rings that are made of appropriate material. Doing so has a 1/3 chance of granting the intrinsic normally granted by the ring as a permanent intrinsic. So for example, you could gain "polymorph control" if you're lucky with a ring of polymorph control.
Wooden rings are also edible, but only by polymorphing into a gelatinous cube.
The main reason to eat rings is to earn their intrinsics without needing to wear the ring. This lets you get more effects, or alternatively avoid the hunger penalty normally associated.
You can't eat rings of slow digestion, but eating rings of conflict, regeneration, and hunger will permanently increase your hunger rate, so be warned if you plan to eat the former two.
For the most part, the intrinsic will remain when you polymorph back to normal. However, the rings that boost a stat, like +Strength, will not remain when you revert. Rings of plus-to-hit and plus-to-damage do revert, and are often eaten by people who specialize in unarmed combat.
I think there are maybe one or two more rings that don't have an effect if eaten (levitation, for example). This is because being able to permanently have some intrinsics is unbalanced, or otherwise makes the game unwieldy to play.
You can also eat amulets. Amulets are all made of iron, so all metallivores can eat them, but they only pass on the intrinsic on a 1/5 chance. Do note that eating an amulet of life saving or an amulet of reflection will have no effect, so don't waste an awesome amulet thinking it will. As well, eating the Eye of the Aethiopica will only confer its base item ability as an amulet of ESP.
Best Answer
Yes, let the pets eat!
Pets gain tameness eating. The only time you might not want them to eat (other than the obvious you want the intrinsic) a corpse is when there are other enemies around however I think they'll attack first and eat later.
Sometimes you might want to get rid of a corpse - a troll for example, pets are ideal for this!.
However, pets cannot get intrinsic's by eating - however some are born with them (such as dragons).