Revert "Make sure to call back reportFinish() on the desired Handler."

This reverts commit 16e2c7b5.

It turns out that I1181e067aa5bedbdf0c7ec1bcec479257aea511c caused
a serious regression Bug 27824691.  To revert that CL, we have to revert
this one first.

Bug: 25332806
Bug: 27824691
Change-Id: Iadfc226eb91cc969b77c9d98e04ec3c76fe86ead