As a newcomer to the industry of soap, my opinion may be considered 'less valid'.
However, as an artist of over 10 years working with clays, slips, oxide stains, and mixing glazes, my perspective of 'natural' may also differ from the average user. I have also exclusively used naturally occurring pigments in my encaustic paints.
'Natural' to me means that it is of the Earth, not a chemical production (eg. lab created dyes, plastics, and other chemically engineered items). Oxides are
naturally occurring in nature. YES oxides go through a lab, but it is to
ISOLATE the oxide and
purify the pollutants from them. This would be like running muddy water through a filter to get drinkable water. They aren't created by chemical process in the lab! If you had the right tools and knowledge, you could isolate these same oxides in nature yourself, as the Chinese did with cobalt oxide for their china at least 1000 years ago. (Although you won't see me suggesting that we use cobalt oxide for topical use either, it's just an example.
)
In conclusion, items found in nature are natural, literally. You can be a snob about it and thumb your nose at natural pigments like those others you have heard, but the distinction is ultimately yours to make - is it natural ENOUGH?
P.S. Those clays you are using for natural pigments? Yeah, they're colored like that because they contain naturally occurring oxides. ALL kaolin that isn't white has had at least one oxide added to it for color. Kaolin is naturally white. (Yeah, I did say that I've worked with clay for over 10 years, didn't I?
) I just thought you should know!!