Statistics is based on the segmentation labelmap as you are seeing in the 2D slice view. What you’re showing in the 3D view is the segmentation with a smoothing factor applied for display purposes only. It is not removing actual features in the segmentation.
Segment Statistics module can compute metrics from both the binary labelmap and closed surface representations. Some metrics, such as surface area are better computer from the smoothed surface. Volume can be computed from both.
If you just want to compute surface area of a 2D area (and not a 3D structure) then it may be simpler to use Markups module: create a closed curve and enable “area” measurement in the Measurements section.
Yes this is because I almost always use binary labelmap statistics plugins. If you the plugins those based on the closed surface then yes what you see in the 3D view is going to be used for statistics.