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It was suggested to make the parent OmniboxResultView the recipient
of button presses. This CL makes that change, and minor clean up to
privatize methods which no longer need to be public.

Bug: 780835
Change-Id: If124040f26a41839fad9518bac1be23c3f52cf88
Reviewed-on: https://chromium-review.googlesource.com/990788
Commit-Queue: Kevin Bailey <krb@chromium.org>
Reviewed-by: Justin Donnelly <jdonnelly@chromium.org>
Cr-Commit-Position: refs/heads/master@{#547971}