It’s still an evidence based stance, but temporarily substitutes one form of evidence for another. The notion of reputation is itself built on evidence, e.g. we observe that someone is generally truthful, so we are later justified in concluding that they might be telling the truth.
The concept of the benefit of the doubt still relies on this form of evidence. That doesn’t imply that this is sufficient.
Regarding Hersh vs. Joe Blow, there is still a meaningful difference in them getting things wrong.
When it’s Joe, you don’t care to begin with, and the revelation of wrongness doesn’t change your opinion of Joe.
When it’s someone like Hersh, such a revelation brings reputational harm, and raises more questions about how he became so convinced of this information to begin with.