I do want to add that a lot of predators also eat the stomach of their prey and there for everything they ate and since most of their prey are either herbivores or omnivores they do consume some plant matter.
Most of the better quality cat foods I see that have veggies in it has like 80% - 95% meat and the rest vegetables, which I think tries to simulate the natural consumption of plant matter.
A lot of cats also eat grass on their own since the fiber helps with digestion.
Yeah, grass can help in both directions. My long haired cat likes to have constant access to grass, it actually makes her puke less. My guess would be that the fiber helps to break up the hair clumps and move them faster down the digestive tract. But I've also had cats who only ate grass to make themselves puke.
Probably depends on the individual cat.