(Note: It's entirely possible that one or more of the premises of this question is incorrect; if that's the case, I would very much appreciate any clarification of what the actual underlying halacha is.)
My understanding is that it is permissible to use eggs and (non-chocolate) milk on Passover, even without a KLP certification, provided they were purchased before the holiday, and that the reason for this permission is that any trace amounts of chametz that might be present become bittul before the chag begins. (Incidentally, I have also heard the same argument given with respect to olive oil, orange juice, and sugar, but there seems to be less consistency in this regard.)
But I have also been told that when purchasing quinoa, it is essential to make sure that it is sourced from a producer who ensures that the quinoa does not come into contact with other grains at any point in the harvesting or packaging process, and therefore quinoa can only be used if it is purchased with a KLP hechsher. The same, I am told, applies to ground spices.
Why doesn't the same principle that permits us to use eggs or milk without a KLP (provided it was purchased before Pesach) also apply to quinoa and spices — or, for that matter, tomato paste, apple juice, amaranth, or other non-kitniyot, "single-ingredient" products?