Non-Hechsher Kashrut

The question is very strong and important and the answer seems vague and possibly misleading.
I’m doing some research since I mistakenly ate a Nature Valley chewy granola bar without supervision.
OU said the ingredients are kosher but the equipment not (i.e they cook/prepare other products with non kosher ingredients). Assuming the worst case ( cooking /heating is used in the preparation of the product) how would that be permissible?
(I’m obviously looking for a serious leniency)
Thanks!