I’m using 2.80, and I can’t seem to parent an object to a specific bone the same way Mike demonstrated. It always seemed to parent any object to the same bone.
I found two alternative methods (although I would like Mike’s method to work for me):
Method 1) Go into edit mode of the armature, select the bone you want to parent to, leave edit mode, then proceed to parent the object to the armature.
Method 2) Go into pose mode, from the toolbar go to Edit->(turn off) Lock Object Modes, from here you can select other objects within pose mode, and parent them directly to selected bones.
Hope this helps someone else! Also anyone has an idea why Mike’s method didn’t work for me, I’d love to know!