I actually think of some veggies as not having carbs, such as members of the Brassicaceae Family like brussels sprouts. As you point out this is not true. As a non insulin user it would be more accurate to say zero carbs I need to be worried about, in the quantities I typically consume.
Other veggies like tomatoes and peppers(both green and hot) require me to limit quantities somewhat. I eat these nearly every day and know the quantities I can handle.
The third classification I use is those which cannot be consumed unless quantities are severely limited. For me this would include potatoes and winter squash. In actual practice the quantities of these foods I can handle are so small that I almost never eat them, its just not worth it.
Obviously insulin users need to be more rigorous in their accounting of carbs.