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This CL fixes a tsan data race, which is caused by calling StopFetchingData
from different threads. It must not be allowed. Use the same thread by using
a PostTask.

BUG=673760
CQ_INCLUDE_TRYBOTS=master.tryserver.chromium.linux:linux_chromium_tsan_rel_ng

Review-Url: https://codereview.chromium.org/2569763004
Cr-Commit-Position: refs/heads/master@{#439798}