Sure:

Edit: Did a fast test: just removed the boolean intersection thing, now I can select all the points. So this part seemed to somehow inherit to everything?
Edit2: Readded the boolean intersection - this time via a clean extruded circle from within MoI as you suggested. (Works great!) The result is the same though - as soon as this cut is in, I cannot show any points anymore. Also added that one (oddshape3-3dm). might be easier to analyze from within MoI.