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

views/controls/scrollbar/native_scroll_bar_win.cc

 // Copyright (c) 2010 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 "views/controls/scrollbar/native_scroll_bar_win.h"
 
 #include <algorithm>
 #include <string>
 
 #include "base/message_loop.h"
@@ skipping 198 matching lines @@
     // cases including when the container is no longer connected to a
     // widget tree.
     DestroyWindow(sb_container_->hwnd());
   }
 }
 
 ////////////////////////////////////////////////////////////////////////////////
 // NativeScrollBarWin, View overrides:
 
 void NativeScrollBarWin::Layout() {
-  SetBoundsRect(native_scroll_bar_->GetContentsBounds());
+  SetBoundsRect(native_scroll_bar_->GetLocalBounds());
   NativeControlWin::Layout();
 }
 
 gfx::Size NativeScrollBarWin::GetPreferredSize() {
   if (native_scroll_bar_->IsHorizontal())
     return gfx::Size(0, GetHorizontalScrollBarHeight());
   return gfx::Size(GetVerticalScrollBarWidth(), 0);
 }
 
 bool NativeScrollBarWin::OnKeyPressed(const KeyEvent& event) {
@@ skipping 110 matching lines @@
 int NativeScrollBarWrapper::GetHorizontalScrollBarHeight() {
   return GetSystemMetrics(SM_CYHSCROLL);
 }
 
 // static
 int NativeScrollBarWrapper::GetVerticalScrollBarWidth() {
   return GetSystemMetrics(SM_CXVSCROLL);
 }
 
 }  // namespace views