As well as the site mentioned earlier (for online newspapers), there are two more, in case you would like to try additional resources for any mention of Mr. Harry.
http://chroniclingamerica.loc.gov/and Amador County Local Newspapers
http://www.amadorgov.org/departments/library [highlighted in blue, near the top-middle of the page]
I have never used this resource before, and I'm always cautious about unknown sites after losing two computers due to viruses, so I am not recommending it, but letting you know it is available.

The Amador Dispatch does have several newspapers for August 1873. After a quick scan of the 9-Aug-1873 newspaper, I didn't see anything about Mr. Harry's and Mr. Skinner's naturalization, but that event could have been so common that it wasn't newsworthy.
While researching, I did find a site that stated the population in Jackson in 1870 was just over 2,400; not a large town.
Mr. Harry may have temporarily lived in a hotel in 1870 (since there were a number of (mostly) men living at the same residence and the first person listed had the occupation of Keeping Hotel. Could they have been passing through at the time and were conveniently recorded there; could they have actually lived there; could they have settled with other miners in a neighbouring town or even lived near the mine in which they worked.

If you find additional information, I would be very interested in hearing. If you have any other questions, please do let us know. Kind regards, Lisa
PS Taking another look at the 1870 census:
"Inhabitants in
Township No. 1". Post Office:
JacksonPerhaps you or others might know - could "Township No. 1" have been outside of Jackson? Something to keep in mind if you continue researching this man.