It should be happening.
In Animate Mode:
When you hover over an image in the viewport, the parent bone should get highlighted.
The parent bone will be selected when you click on the image.
As Shiu described, it won't happen if you disabled Bone Selection in the Options box. (It's that small 3x3 table of dot toggles next to the Compensation tools).
The arrow column enables selecting items. The eye column means visibility. And the tag column means name labels.
This might be a little bit of an obscure detail though: You have to make sure to DESELECT your currently selected bone (you can use spacebar) to be able to select a bone again by clicking on its child image in the viewport. Otherwise, clicking only applies your currently active tool (ie, Translate, Rotate, Scale).
