Cats eat grass for medicinal reasons, much as Black Sheep says.
Animals that live on grass, herbivores in general, do have longer intestines and big stomachs. Ruminants have an extra stomach and chew the cud, for the simple reson that grass takes a lot of breaking down.
Of course lions won't eat straw. My cats regularly chew a bit of grass, and usually choose to come indoors and if they can, go to sleep on a nice cushion on the settee before vomiting it up, but if I started feeding them grass at teatime they'd look at me as if I'd lost my head.
The whole JW thing about Paradise Earth is BONKERS. They really belieive it, but it is utter rubbish!