Just to illustrate further with your particular file - take these 2 adjacent hexes for example:



If you turn on control points for that selected hex, you'll see that the points are actually 4 corner points somewhat larger than the hex itself like this:



That hex is a trimmed surface - the "underlying surface" is a simple 4 corner plane and the hex edges are trim edges that are marking the outer boundary of what to trim away from the outside of the plane to make the final shape.

When you manipulate those control points, you are manipulating the shape of the "underlying surface" plane, like for example dragging the corner point will do this:



Notice there that after dragging that point there is a gap opened up between the hex pieces - that's why points do not show when you have joined pieces like this together, because dragging on them would normally open up holes between what was supposed to be a shared common edge.

If you turn on control points for the other surface, you can see that the control points of the 2 surfaces are not really aligned or touching with one another in any way - it's the trim edges that actually touch each other:



Hope this helps explain it!

- Michael