Tomatoes are from the toxic Nightshade family of plants like white potatoes, eggplant, tomatillos, chili and bell peppers, goji berries, some huckleberries, etc etc, the list goes on and on. I think even cilantro and celery happen to be nightshade related. There are over 2500 plants in the nightshade family and I don't believe any of them need bee pollination. Not all parts of nightshade plants are toxic -- for instance, tomato vines and leaves are toxic to humans, animals, and most common garden insects, and the peels and seeds have high concentration of lectin that bothers digestive processes (we limit our beans and cashew nut intake because of the lectin in them), yet the meat of a tomato is quite safe. Therefore, when I freezer-store my garden tomatoes I blanch and peel off the skins and scoop out the gel and seeds before freezing. I'm sure you've all heard how toxic the green uncooked potato peels are for chickens -- we stay away from deep orange holiday yams as well but use the light-skinned sweet potato instead for our mashed potatoes.
My chickens won't touch nightshade celery, bell peppers, cilantro, or any of the cruciferous veggies like kale, cabbage, brussel sprouts, broccoli or cauliflower cooked or not -- from what I've researched the cruciferous veggies play some havoc on the thyroid so we don't bother giving these veggies to family or pets either. Everyone's digestive system is different and can tolerate nightshade or cruciferous veggies but we've decided with our allergies it's best for ourselves to limit them.