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

views/view.cc

 // Copyright (c) 2011 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/view.h"
 
 #include <algorithm>
 #ifndef NDEBUG
 #include <iostream>
 #endif
@@ skipping 557 matching lines @@
   if (parent_) {
     // Translate the requested paint rect to the parent's coordinate system
     // then pass this notification up to the parent.
     gfx::Rect paint_rect = r;
     paint_rect.Offset(GetMirroredPosition());
     parent_->SchedulePaint(paint_rect, urgent);
   }
 }
 
 void View::SchedulePaint() {
-  SchedulePaint(GetContentsBounds(), false);
+  SchedulePaint(GetLocalBounds(), false);
 }
 
 void View::Paint(gfx::Canvas* canvas) {
   PaintBackground(canvas);
   PaintFocusBorder(canvas);
   PaintBorder(canvas);
 }
 
 void View::PaintBackground(gfx::Canvas* canvas) {
   if (background_.get())
@@ skipping 979 matching lines @@
   OSExchangeData data;
   WriteDragData(press_pt, &data);
 
   // Message the RootView to do the drag and drop. That way if we're removed
   // the RootView can detect it and avoid calling us back.
   RootView* root_view = GetRootView();
   root_view->StartDragForViewFromMouseEvent(this, data, drag_operations);
 }
 
 }  // namespace views