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

chrome/browser/ui/views/info_bubble.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/info_bubble.h"
 
 #include <vector>
 
 #include "chrome/browser/ui/window_sizer.h"
 #include "chrome/common/notification_service.h"
@@ skipping 95 matching lines @@
 void BorderContents::Paint(gfx::Canvas* canvas) {
   // 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(InfoBubble::kBackgroundColor);
   gfx::Path path;
-  gfx::Rect bounds(GetLocalBounds());
+  gfx::Rect bounds(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);
 
   // Now we paint the border, so it will be alpha-blended atop the contents.
   // This looks slightly better in the corners than drawing the contents atop
   // the border.
@@ skipping 431 matching lines @@
     animation_->Hide();
 }
 
 bool InfoBubble::AcceleratorPressed(const views::Accelerator& accelerator) {
   if (!delegate_ || delegate_->CloseOnEscape()) {
     DoClose(true);
     return true;
   }
   return false;
 }