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When the Web Request API was moved to the UI thread, there was a fair
amount clean up to do be done. This CL cleans up a bit more.

Bug: 980774
Change-Id: I6a4ab52eda0508aa14c677a6fd5fddc393d3e570
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1982687Reviewed-by: Devlin <rdevlin.cronin@chromium.org>
Commit-Queue: David Bertoni <dbertoni@chromium.org>
Cr-Commit-Position: refs/heads/master@{#728086}