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Not sure what (or who) fixed it, but it's no longer flaky. Adding a
simplified and non-flaky test that also passes now.

Bug: 1066640
Change-Id: Ia82810e240eab6f3ee955afe89ebeeffebf808d2
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2339521Reviewed-by: Ian Kilpatrick <ikilpatrick@chromium.org>
Reviewed-by: Koji Ishii <kojii@chromium.org>
Commit-Queue: Morten Stenshorne <mstensho@chromium.org>
Cr-Commit-Position: refs/heads/master@{#795379}