Whoever told you that, probably they don't know what they're really talking about. Having said that, there are always poisonous plants or some veggies that are jusg no good for rabbits, like iceberg salad. Stiff ones like carrots should be fed in moderation due to sweetness and cabbage due to being gassy. Nonegheless, Veggies are important in a rabbit's diet. Try by offering yours some romaine lettuce. Look up the forum for safe veggies and what people give their rabbits for vegs.
A domesticated rabbit is called a rabbit, or "bunny" in casual. A "hare" would refer to a wild rabbit.
If you have a domestic pet rabbit, it is a rabbit (some like to call it a bunny) but would not be a hare. What country are you in?
Domestic rabbits' diet depends on their age and background. Typically, a rabbit at least 12 weeks of age can begin to be fed greens along with unlimited hay and some plain juvenile pellets. Greens are supposed to be introduced slowly so bunny's tummy can adjust to the new foods.
Once a rabbit is 6 months of age, it should transition to an adult diet:
Unlimited grass hay
measured plain pellets (1/4 c for a 5-7 lb rabbit)
2-4 cups of daily greens