bitul & bdi'eved

Question

kavod harav, when i discuss your tshuvot with defenders of the hashgacha industry they argue that bitul, only applies bdi'eved. two questions: a)is this always true, and what are the sources either way? b)how does bdi'eved work? Is it related to the 'cheftza', ie the lard in that product was only used as a processing agent to help get the dried fruit off the drying conveyor, it has no taste in the final product so it's use is only bdi'eved, or does it apply to the 'gavra' ie I am starving and only see thai fish sauce in front of me, I can with pretty good confidence know that any oysters accidentally put in the mix is less than 1/60th so bdi'eved I can drink thai fish sauce to save my life? Perhaps my logic is not right at all, but I need to understand these issues before I can undo years of hashgacha industry indoctrination. I thank you very much for your reply.