A wild rabbits diet consists of mostly roots, barks, and dried grasses, not greens. They do nibble on them, but don't eat that many. When you see a wild rabbit out in someones yard, more than likely they are eating the roots of the grass, not the grass itself. Wild rabbits are also a different species than our domesticated rabbits. Domestic rabbits are dubbed "European" rabbits because they originated in Europe. They cannot produce offspring with a wild rabbit. They can breed, but nothing will come of it.
I second the oats. Plain oatmeal is great, but in small quantities. When introducing a new food, go slowly, and only introduce one new food per week (that's what I recommend anyway). That way, if there are problems, you can easily identify which plant or feed item is causing it.
Hope this helps some!
Emily