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This relands commit 7a5df8d5

Reverting didn't fix the test, and the test was also found to have been
flaky before the original commit.

Bug: 268984, 990692
Change-Id: I26c8c264e345e0cec6e0677e9fd28517f96d0504
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1748603
Auto-Submit: Evan Stade <estade@chromium.org>
Commit-Queue: Avi Drissman <avi@chromium.org>
Reviewed-by: Avi Drissman <avi@chromium.org>
Cr-Commit-Position: refs/heads/master@{#687392}