I would expect this to happen on a regular basis purely by chance. People routinely lose their rings while gardening. If you lost a ring in a bed where you always grow root vegetables, eventually one of those vegetables is going to engulf that ring, if you wait long enough. (If you lost it in a bed of not-root vegetables, one of them is likely to engulf the ring in its roots too, but you’d be unlikely to ever know it.) It’s a lot more credible than those “I lost my ring in this body of water, then found it in a fish I caught” stories.
Yeah, I suspect it’s the sugar in the carrots that’s quite enticing (or has been to the dogs I’ve owned, anyways).