The mitigations look very different for the "knowingly" vs "unknowingly" cases. For example, amplified oversight and interpretability are both based on the idea that we can extract the relevant knowledge out of the AI system -- this of course only works if the AI system knows the relevant information in the first place. In contrast, if the AI system doesn't know it is making a mistake, one of the best mitigations is to make the AI system more capable so that it does realize this and then doesn't make that mistake.
So it's at least useful to distinguish between the "knowingly" and "unknowingly" cases. In practice, our team focuses on the "knowingly" case because that is where a lot of the most severe risks arise, and because the "unknowingly" cases tend to improve by default as AI capabilities improve.