Vessels and Taste

Question

Shalom. What are the halachot that kashrut organizations rely on to assign DAIRY status to products that contain NO dairy ingredients? Are the kelim (mixers, bowls, etc.) mamash dairy, i.e., there are actual milk products contaminating the parve batch to such an extent that the parve product is now dairy? Considering the volume of the batches required to make 100,000 cookies, that would be a lot of dairy remaining behind. Are the ovens dairy, i.e. used for other runs that are mamash dairy? If a parve product is baked in a clean dairy oven, does the product become mamash dairy or only 'taam' dairy? Perhaps the parve products are baked with mamash dairy products at the same time? What if the oven has mamash dairy material spilled all over it? (one would think that even with spilled milk in the oven, the oven would burn off the milk rendering it no longer dairy) I am not asking these questions to throw skepticism at kashrut organizations, but rather to understand the halachot on which they base their hashgachic decisions. For example, how do Triscuits, which were once parve, now become dairy, with no change in the ingredient list? Thank you for your help.