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Its one remaining member, GetOmniboxView, can be replaced easily by
telling the SearchTabHelper when its tab gets attached to a new window
(i.e. Browser::TabInsertedAt), at which point it can grab the
OmniboxView* itself. This also correctly handles the case where a tab
is dragged between windows.

BUG=627747

Review-Url: https://codereview.chromium.org/2739943005
Cr-Commit-Position: refs/heads/master@{#456046}