Understanding distance fields

The initial problem I had is described here: https://answers.unrealengine.com/questions/350101/is-it-possible-to-draw-objects-which-are-sliced-by.html

With “regular” materials, you can see how the static mesh plane intersects the sphere, cube and cone:

In my case, the sphere, cube and cone are transparent/invisible. I depict this with a grid:

76081-transparent_objects.png

I would like to paint the area where the static mesh plane intersects the sphere, cube and cone, like this:

I believe that this can be achieved by covering the static mesh plane with my DistanceToNearestSurface-material if I configure it in the correct way.
I.e. following the logic:

IF inside sphere/cube/cone
  THEN color = red
  ELSE color = white

It should be possible to determine “inside” using DistanceToNearestSurface, right?

I hope this is clearer now. Otherwise please tell me and I will try to clarify more.