assur b'mashehu

Question

Please correct me if I am wrong. A chametz containing product bought before Passover, can be eaten on Passover if that chametz is less then 1/60 of it, because chametz bought before Passover is bittul b’shishim. However, a chametz containing product bought on Passover, can not be eaten (or bought) because chametz on Passover is assur b'mashehu (forbidden in small amount). Now, kashrut qualified by ingredients only, if I understand it correctly, is based on the idea that any less-then-kosher ingredients are rendered insignificant, thanks to the strict standards of our FDA; bittul b’shishim. Therefore, even if a product has trace elements of forbidden foods, it is as if they are not there. Yet, you are allowing us to buy and eat these same products on Passover despite the possibility of trace elements of chametz, which is assure b’mashehu. Are those foods in question permissible because chametz is bittul b’shishim even on Passover, or because the trace elements of chametz found in those foods is less then a mashehu (whatever a mashehu is)? This entire premise of this question could be wrong, because, knowing no Hebrew, I cant look up the original sources, so please guide me. Thanks for the clarity.