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Instead it now always has a MessageLoop* and is allowed to use APIs
which will soon no longer be exposed on MessageLoop::current().

This is a precusor cleanup extracted from
https://chromium-review.googlesource.com/c/chromium/src/+/957760/7
in the broader effort to restrict usage of MessageLoop::current().

R=haraken@chromium.org

Bug: 825327
Change-Id: I580fe360ff9630a5ffb40b89921c6889d449e67a
Reviewed-on: https://chromium-review.googlesource.com/986813
Commit-Queue: Gabriel Charette <gab@chromium.org>
Reviewed-by: Kentaro Hara <haraken@chromium.org>
Cr-Commit-Position: refs/heads/master@{#548163}