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Standard context menu options aren't available in profile picker web
contents. For example, "View page source" and "Inspect" don't work at
all in the system profile.

This change also helps fix the bug when the profile picker window closes
after dismissing the context menu (I don't know what's the cause of this
though).

Bug: 1121543, 1121541
Change-Id: Iad91145481c8b5d8184f0bf600cea5a8a39f158c
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2374451Reviewed-by: David Roger <droger@chromium.org>
Commit-Queue: Alex Ilin <alexilin@chromium.org>
Cr-Commit-Position: refs/heads/master@{#801477}