Note that I have the "Spline Toolbar" turned on. Also, I am drawing a "style spline". When I highlight that spline, the spline toolbar does not show any icons to show or hide the handles.
If I draw a regular spline, it has the icon ghosted, and it has no effect if I click it. I should add, that if I click the "show inflection" icon, it will show the inflection point, but if I re-click that icon, I cannot make the inflection point symbol go away. It seems that once you show it, you are stuck with it.