It's in ~ProfileImpl(), so looks like just some forgotten base::RunLoop::RunUntilIdle() to let things shutdown, and hopefully not a privacy issue.

 Issue 737893  has been merged into this issue.

Looking at other builders, I didn't find the exact same issue on other platforms, but I did find an instance of it timing out and succeeding on retry on windows:
https://luci-logdog.appspot.com/v/?s=chromium%2Fbb%2Fchromium.win%2FWin10_Tests_x64%2F13372%2F%2B%2Frecipes%2Fsteps%2Fbrowser_tests_on_Windows-10-10586%2F0%2Fstdout

Based on the stack in crbug/737893 it looks like this is some kind of crash during BrowserProcessImpl::StartTearDown(), inside
browser_sync::ProfileSyncService::Shutdown()

+skym in case that looks familiar

My understanding at this point is that this actually a test timeout rather than a crash, and the step that is taking a long time is sync_thread_->Stop() during Shutdown() in the test teardown, so this is after all of the actual checks of the test have passed successfully.

I have a CL open to disable the test: https://chromium-review.googlesource.com/c/556242/

I have a theory that this could be fixed by calling RequestStop on the sync_service at the end of the test, because SyncTest does that on the profiles it creates during TearDown, and not on the service enabled in this test, but I'm trying to make sure that I can repro this on a test bot and confirm that change fixes the problem.

I think we should probably just disable the test for now.

Seems to be flaky on Windows and Linux too.

https://test-results.appspot.com/dashboards/flakiness_dashboard.html#tests=UkmBrowserTest.Incognito

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/bb5f3653b6fa4cae8dba0580e6655b68a5b73e79

commit bb5f3653b6fa4cae8dba0580e6655b68a5b73e79
Author: Steven Holte <holte@google.com>
Date: Fri Jun 30 03:09:59 2017

Disable flaky UkmBrowserTest.IncognitoCheck.

Bug:  737682 
Change-Id: If1da9646ef0bce32b2055823df01113196252795
Reviewed-on: https://chromium-review.googlesource.com/556242
Reviewed-by: Timothy Loh <timloh@chromium.org>
Commit-Queue: Steven Holte <holte@chromium.org>
Cr-Commit-Position: refs/heads/master@{#483612}
[modify] https://crrev.com/bb5f3653b6fa4cae8dba0580e6655b68a5b73e79/chrome/browser/metrics/ukm_browsertest.cc

Thanks, removing from sheriff queue since it's been disabled for now.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/c5aeb440d84ce37b5c8a1d8f5bc185479b325665

commit c5aeb440d84ce37b5c8a1d8f5bc185479b325665
Author: Steven Holte <holte@google.com>
Date: Fri Jun 30 21:22:20 2017

Fix UkmBrowserTest.IncognitoCheck

Bug:  737682 
Change-Id: I37333be358a82883ba3d4098e8a3fa8d103671c0
Reviewed-on: https://chromium-review.googlesource.com/557422
Commit-Queue: Steven Holte <holte@chromium.org>
Reviewed-by: Sky Malice <skym@chromium.org>
Cr-Commit-Position: refs/heads/master@{#483824}
[modify] https://crrev.com/c5aeb440d84ce37b5c8a1d8f5bc185479b325665/chrome/browser/metrics/ukm_browsertest.cc

The extra cleanup steps in the test appear to have fixed it.  I haven't seen any failures related to this on the bots after re-enabling the test.