The first question you should as is what is a correct map? to log a cache near the border of areas are always a risky plan to have a found in that county because of incorrect border on different maps and pgc data scources. And the cache can be moved a couple of meters after you found it
The only map on geocaching website with border i can see without map extensions are osm via MapQuest. That puts the cache 129 m inside fisher county
I would not really trust borders on google maps borders been more the 10km off and OSM maps that are really incorrect too.
If i use the USGS topo maps puts the border is 120 m further to the east.
Google maps show no county borders but google earth puts the cache 12 m inside jones county
Bing maps is the first to use a non straight line for the border between the counties and puts it 200 m east of the cache bur identifies the coordinates as in Jones county
Maps from us census bureau puts the cache 2 m inside Fisher county but they only have a acccurency of 5 metes
The census data an google earth is almost the same and and has might the same source that pgc uses.
I would not necessary trust the sign on the road. You have now idea how accurate it was placed along the road. It might have been placed along the road when the county was created in 1876 and i suspect the maps and precition at that time was not that high. From google street view it is 120 m along the road from the cache
the osm border/map intercection is 500 m from the cache
and the USGS 840 m
And in the census and google easth it is a few meters south and north if the cache.
What county the cache is in really depend on the definition on counties in Texas. It still might be impossible to know depending on the definition.