The "leafy greens" advice often comes from house rabbit people. They sometimes have concerns about their rabbits being overweight on an all-pellet diet. Unfortunately, people often interpret "leafy greens" to mean lettuce and cabbage. Iceberg lettuce is pretty much useless as rabbit feed and can cause digestive problems, especially if the rabbit is not accustomed to it. Leaf lettuce is better but it still does not have much food value. Cabbage is quite nutritious but can cause gas. It must be introduced gradually.
Garden greens have a place, but "leafy greens" would be better interpreted as "broad-leafed safe weeds." Not everyone has access to these or the knowledge to select them wisely. This is changing and I think RT has had a role in making information available.
All changes in diet should be made gradually. I have transitioned quite a few rabbits from pellets to natural feed and most manage the switch fairly well. In the next generation, where the kits have access to natural feed including lots of green leafy weeds from the beginning, I have never seen a problem.
See the Safe Plants for Rabbits sticky in the Natural Feeding forum for a starter list of safe plants. Use the Latin names to identify them before feeding; common names are often regional.