Not sure I understand your point, he is not being indicted for publishing false information. Assuming he never did, why would that make the charges bullshit?
As you note, it’s irrelevant but also, if true, illustrates how selectively showing true info is deceptive.
[0]https://www.theverge.com/platform/amp/2016/9/9/12864328/wiki...
If you don't believe that Assange has done truthful hard-hitting journalism, or you believe that he isn't a journalist at all, then you can maintain the belief that we don't put journalists in prison while sitting idle as he rots in prison, because he is not a True Journalist. "We wouldn't do that to True Journalists. Assange is different."
Example, as a journalist you cannot just walk into a US Army base and start reporting.
I don't know if that meets your definition of public oversight.