Politics vs. Halacha

Question

Kavod Harav: A relative of mine is a mashgiach and always said that the Kashrut certifying boards in this country, we all know who they are, are involved in political game playing due to the amounts of money involved. Kashrut is big business and in any free market system who have your honest businessman, your in-between, and your downright defrauders. Putting that aside, without a hashgachah, please explain how reading the ingredients of a product is a way of ensuring kashruth? Please understand that by asking such a question I am not doubting your competence as an expert in Kashrut. Rather, it is for my own educational purposes. My only problem is that without a mashgiach (or any competent supervisor for that matter), if items are made with kosher ingredients, but manufatured or processed on machinery or in plants where non-kosher products have been processed, etc., does that not pose any problems? Todah Rabah.