I think that the case makes a difference. "The factory is not here" = something resembling "Завод не здесь" or "Завод здесь нет". There is a factory, it's just not here. Нет завода on the other hand indicates that there's no factory here, with no idea whether it even exists somewhere else. I think.
I think you are correct, but in your second example, I think завод needs to be in the genitive. 1. Здесь нет завода. = There is no factory here. (завод is in gen for non-existence) 2. Завода здесь нет. = The factory is not here. (implies the factory is gone; maybe a tornado hit it or something. Thus, завод is again in gen for non-existence) 3. Завод не здесь. = The factory is not here. (BUT it is implied that it does exist somewhere else, just not here. Hence, завод is in nominative.)
Ha, I found a whole article about that... in Russian. Google Translate amusingly renders its title, "What is the difference between a factory and a factory?"
(Чем отличается утка?)
ФАБРИКА A factory is an enterprise with an automated production cycle and a relatively large number of workers. Products are manufactured in bulk, and individual units of each of them do not have individual features. The factory is a new milestone in the development of industry compared to the craft workshop where the final division of labor occurred.
ЗАВОД A plant is an industrial facility engaged in production, or an enterprise that breeds horses and other pedigreed animals. The most important attribute is a complete automated cycle, involving minimal human involvement. In the literature, plants often refer to those objects where the means of production are produced. Deep processing of raw materials involves a minimum amount of waste.