Ingrediant Checking

Question

I notice that you are willing to consider something "kosher" simply by looking at the ingrediants... This doesn't take into account that the machines may have been previously used for unkosher products. I know any remains of other products would be less than 1/60th, but doesnt that only apply in cases where the 1/60th is either by accident, or where we cant find out? Or does it still apply in a case where we simply choose not to investigate further?