You’re taking “it’s possible to be clean after bathing without soap” as a way stronger statement than it is.
Do you think I’m saying soap is bad?
No one is talking about hygienic hand washing practices for medicine, food prep, after defecation, or after being coated in tough substances.
We’re in a giant pile of people talking about routing bathing to prevent body odor and the skin issues caused by poor bodily hygiene.
Washing with running water and a scrubbing action is sufficient for that purpose for many people. Bathing without soap is not a guarantee that you will have BO, a rash, skin lesions, or acne.

The Africa point isn’t really the gotcha you think it is. Soap working better faster doesn’t mean that a lack of soap doesn’t work. As you said, when they didn’t have soap they still washed. People are generally interested in being clean, and pragmatic. They’ll clean themselves, and if something helps them get cleaner faster, they’ll use it.

And yup, that passage does document that the Roman empire eschewed soap for personal hygiene until roughly year zero.