Geocaching.com uses the state selected by the CO. It is not determined by the coordinates.
GSAK uses the gc.com data if you dont ask it to recacluclate the state.
If it changes on corredted is configurable if I am not mistaken
I would not trust the borders on google maps they are often incorrect. I have logged a cache on a border in Sweden that was 12 km from the border on google maps
In the US i would trust the USGS maps that are by definition correct if I man not mistaken.
Can be added with Geocaching Map Enhancements http://geo.inge.org.uk/gme.htm
pgc uses the tiger polygons in the us if I am not mistaken
If you change the map to osm the left borde line on the map it tagged that is uses tiger as source.
If i am not mistaken it more often the CO have set the incorrect state then the polygons are incorrect. But there will often be problem nere the borders.
A reason to calculate the state is because the countys are calculated from the polygons and it would be strange if the cache was in Washoe County (NV) and in califonia in the data
And always log a cache not on the border to get a new county, You never know if ti is moved or the polygonsa are updated. I would find a cache a few hundred meters from the border to be sure