Revert of Revert of Refactor to not actually update composited layer mappings when called outside of RenderLayerComposi… (https://codereview.chromium.org/159783004/)

Reason for revert:
We determined that this CL did not actually cause the failure.

Original issue's description:
> Revert of Refactor to not actually update composited layer mappings when called outside of RenderLayerComposi… (https://codereview.chromium.org/142973009/)
> 
> Reason for revert:
> Appears to have broken a large number of content_unittests and browser_tests in Debug:
> 
> http://build.chromium.org/p/chromium.webkit/builders/Linux%20Tests%20%28dbg%29/builds/1620
> 
> Original issue's description:
> > Refactor to not actually update composited layer mappings when called outside of RenderLayerCompositor,
> > and instead register dirty bits for a later update.
> > 
> > BUG=339892
> > 
> > Committed: https://src.chromium.org/viewvc/blink?view=rev&revision=166872
> 
> TBR=shawnsingh@chromium.org,vollick@chromium.org,ojan@chromium.org,eseidel@chromium.org,ch.dumez@samsung.com,chrishtr@chromium.org
> NOTREECHECKS=true
> NOTRY=true
> BUG=339892
> 
> Committed: https://src.chromium.org/viewvc/blink?view=rev&revision=166929

TBR=shawnsingh@chromium.org,vollick@chromium.org,ojan@chromium.org,eseidel@chromium.org,ch.dumez@samsung.com,abarth@chromium.org
NOTREECHECKS=true
NOTRY=true
BUG=339892

Review URL: https://codereview.chromium.org/148293013

git-svn-id: svn://svn.chromium.org/blink/trunk@166933 bbb929c8-8fbe-4397-9dbb-9b2b20218538