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

chrome/browser/ui/views/bubble_border.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 "chrome/browser/ui/views/bubble_border.h"
 
 #include "base/logging.h"
 #include "grit/theme_resources.h"
 #include "third_party/skia/include/core/SkBitmap.h"
 #include "ui/base/resource/resource_bundle.h"
@@ skipping 415 matching lines @@
 void BubbleBackground::Paint(gfx::Canvas* canvas, views::View* view) const {
   // The border of this view creates an anti-aliased round-rect region for the
   // contents, which we need to fill with the background color.
   // NOTE: This doesn't handle an arrow location of "NONE", which has square top
   // corners.
   SkPaint paint;
   paint.setAntiAlias(true);
   paint.setStyle(SkPaint::kFill_Style);
   paint.setColor(border_->background_color());
   gfx::Path path;
-  gfx::Rect bounds(view->GetLocalBounds());
+  gfx::Rect bounds(view->GetContentsBounds());
   SkRect rect;
   rect.set(SkIntToScalar(bounds.x()), SkIntToScalar(bounds.y()),
            SkIntToScalar(bounds.right()), SkIntToScalar(bounds.bottom()));
   SkScalar radius = SkIntToScalar(BubbleBorder::GetCornerRadius());
   path.addRoundRect(rect, radius, radius);
   canvas->AsCanvasSkia()->drawPath(path, paint);
 }