Remove remaining use of the deprecated MessageLoopProxy

Remove remaining use of the deprecated MessageLoopProxy

This patch removes the remaining usage of MessageLoopProxy outside
base/. Note that there are still some call sites for
Thread::message_loop_proxy() and MessageLoop::message_loop_proxy() which
will be cleaned up separately.

BUG=465354
Committed: https://crrev.com/a3899866682a1e846fc978368b00531a0e21d266
Cr-Commit-Position: refs/heads/master@{#334198}

[Sami, 2015-06-12 13:19:34]

skyostil@chromium.org changed reviewers:
+ jam@chromium.org

[Sami, 2015-06-12 13:20:01]

PTAL.

[jam, 2015-06-12 16:32:21]

lgtm

[Sami, 2015-06-12 16:35:40]

The CQ bit was checked by skyostil@chromium.org

[Sami, 2015-06-12 16:35:41]

The patchset sent to the CQ was uploaded after l-g-t-m from jam@chromium.org
Link to the patchset: https://codereview.chromium.org/1169923009/#ps100001
(title: "Fix typo.")

[commit-bot: I haz the power, 2015-06-12 16:36:23]

CQ is trying da patch. Follow status at
 https://chromium-cq-status.appspot.com/patch-status/1169923009/100001

[commit-bot: I haz the power, 2015-06-12 18:22:08]

Committed patchset #6 (id:100001)

[commit-bot: I haz the power, 2015-06-12 18:22:51]

Patchset 6 (id:??) landed as
https://crrev.com/a3899866682a1e846fc978368b00531a0e21d266
Cr-Commit-Position: refs/heads/master@{#334198}