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In particular, this gets rid of ProfileSyncServiceStartupCrosTest, which
was not meaningfully different from the non-Cros version.
Also adds a few extra assertions and comments.

Bug: none
Change-Id: Iabba34647d084b1518a2cea239c9f25d463aa27b
Reviewed-on: https://chromium-review.googlesource.com/1117073
Commit-Queue: Marc Treib <treib@chromium.org>
Reviewed-by: Jan Krcal <jkrcal@chromium.org>
Cr-Commit-Position: refs/heads/master@{#570807}