Surrounding topography does have an effect on each pixel as it is analyzed using the solar analysis tools. From ESRI's own documentation:
...accounts for atmospheric effects, site latitude and elevation,
steepness (slope) and compass direction (aspect), daily and seasonal
shifts of the sun angle, and effects of shadows cast by surrounding
How the viewshed is calculated
Since radiation can be greatly affected by topography and surface
features, a key component of the calculation algorithm requires the
generation of an upward-looking hemispherical viewshed for every
location in the digital elevation model (DEM).
It would seem that if you are in a mountainous region and you remove some of those mountains, the nearby pixels will be affected. The documentation doesn't mention anything about these edge effects. A test or possible solution to this issue would be to create overlapping clipped regions. You could recombine these clipped regions based on a rule-set (e.g. use the overlapping region that has the lowest pixel values).