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While debugging flaky browser_tests, it was revealed that a
WebContentsVideoCaptureMachine could actually outlive the tear-down of
the BrowserThreadImpl for the UI thread.  Not having been explicitly
stopped first, destructors in the object graph would execute clean up
code that would attempt operations that are invalid after the
BrowserThreadImpl for the UI thread has been torn down.

This change also includes a bunch of minor clean-ups.

BUG=396413

Review URL: https://codereview.chromium.org/514073002

Cr-Commit-Position: refs/heads/master@{#292513}