@Peachy Clean Soap -- I use ROE, rosemary oleoresin extract, as my antioxidant.
@SoapLover1 -- My personal opinion is exactly same as yours, but our opinion is only that -- opinion.
In the USA, plain soap as defined by the FDA does NOT require an ingredients list at all. If you do provide an ingredients list, it is lawful to provide a list that is incomplete or says "may contain" or "saponified fats of".
You can discuss the wisdom of providing a complete and correct ingredients list, but don't insist the law requires all ingredients to be listed for plain soap, because the law does not require this.
An excellent resource for understanding the US rules for labeling is Marie Gale. Or go direct to the FDA and CPSC and read the regulations there.