Thanks Trevor! This is indeed very useful. And not only for newbies, because this is a relatively new feature…
This works whether you use right-click-select or left-click select, because RCS and LCS only affect the selection method in the 3D viewport.
Also, your active object in the above example is the Camera. A bit confusing, I know: it is active, but not selected.
But you are right that the active object stays the active object when box selecting this way in the outliner.