Choropleth incorrect border polygons

I want to add some information on #31 that I gather during the reimplementation of Choropleth. I created this additional issue because I wanted it to be clearly laid out.

The problem of drawing the wrong countries comes from points near the countries borders which are incorrectly assigned because the polygons we use may be incorrect. The problem doesn't come from simplifying them for smaller file sizes. The problem lies in the original data that we use. For levels 0 and 1 that would be http://www.naturalearthdata.com. I tried using un-simplified original data and the borders were still not aligned with the ones drawn on maps (see picture below). I am not sure what the ground truth is, but I would assume that OpenStreetMaps is correct. So the solution to this issue is to find new, more correct border polygon data.

By only googling a bit I could unfortunately not find a better data source. External help from someone who knows more about geodata would be really appreciated.