Highland Pioneer Sketches has a section on a Davidson family in Salem Twp., but I don't see anything in Hamer in that book. The Davidsons in Salem came over from Scotland (four brothers who came were John, Robert, William and Joshua) and some of the family served in the Rev War before migrating to Kentucky and then to Ohio. Mostly it describes the family of John Davidson who appears to have landed in what would be Highland County pretty early on (around 1800?) and was known for doing Salt Mining in the area among other things.

I don't see much that matches with what you gave, so this may be an entirely different set of Davidsons, but I can scan the relevant pages if you want to look into it.