I noted in one of your previous response (“Bishul Akum for a paid housekeeper”) that one can rely on the leniency of the Rashba and the Shach only BEDIEVED, and in those cases, may eat bishul akum of a paid housekeeper.
Can you provide more detail about what scenarios may be “bedieved”? My parents often invite my wife and I for meals, and we know that everything is cooked by the non-Jewish housekeeper without the oven/stove being turned on by a Jew (even after multiple requests from us to my parents). Can we still eat the food for shalom bayit purposes? Would that be considered “bedieved”?
This will certainly qualify as extenuating circumstances, and it will be permitted, under the circumstances, to rely on the lenient opinions.
Because the prohibition is essentially rabbinic in nature, there is greater leeway for leniency.