It turns out I had the sense of the GetLocalBounds bool wrong everywhere, so ...

chrome/browser/chromeos/login/web_page_view.cc

 // Copyright (c) 2009 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include "chrome/browser/chromeos/login/web_page_view.h"
 
 #include "base/callback.h"
 #include "base/logging.h"
 #include "base/string_util.h"
 #include "base/time.h"
@@ skipping 157 matching lines @@
 
 void WebPageView::ShowWaitingControls() {
   throbber_->Start();
   connecting_label_->SetVisible(true);
 }
 
 ///////////////////////////////////////////////////////////////////////////////
 // WebPageView, views::View implementation:
 
 void WebPageView::Layout() {
-  dom_view()->SetBoundsRect(GetLocalBounds());
+  dom_view()->SetBoundsRect(GetContentsBounds());
   int y = height() / 2  - throbber_->GetPreferredSize().height() / 2;
   throbber_->SetBounds(
       width() / 2 - throbber_->GetPreferredSize().width() / 2,
       y,
       throbber_->GetPreferredSize().width(),
       throbber_->GetPreferredSize().height());
   connecting_label_->SetBounds(
       width() / 2 - connecting_label_->GetPreferredSize().width() / 2,
       y + throbber_->GetPreferredSize().height() + kSpacing,
       connecting_label_->GetPreferredSize().width(),
       connecting_label_->GetPreferredSize().height());
 }
 
 }  // namespace chromeos