That's a myth.
I'm glad to hear someone else say this. My Beagle, Daisy, loves to graze on plants and grass. I sometimes call her my giraffe (because she'll stretch her neck to get to a plant)! This never makes her sick.

I hope the vet is able to figure out what is going on with Coco. It is so frusturating when you can't figure out what to do to help them.