Personally I think the benefits of providing fresh wild forage to bunnies outweighs any risk of them catching anything detrimental.
You will never be 100% sure that anything you pick hasn't been contaminated, although that is also probably true for hay. However, there are certain precautions you can take. I feed forage daily to my bunnies and most of that comes from within my garden, so I would hopefully be aware if there were also wild bunnies there. I rarely wash the plants, but do inspect them, especially for bird droppings, which if found, will mean that I completely discard that leaf. If I was picking forage from the countryside, I would try to avoid areas where I know there to be wild bunnies. I would also avoid areas where I know there to be dogwalkers. I wouldn't pick from the side of a road either, because of traffic fumes. Washing plants will make them clean, but not disease free.
Other thoughts are to be really sure of your identification of a plant. Also consider suitable tree leaves and sticks, which are very beneficial, both to teeth and digestion, and which will not have been contaminated by wild bunnies or dogs.