No need to suppress ZoomBubble if !window_->IsActive().

chrome/browser/ui/browser.cc

 // Copyright 2012 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/browser.h"
 
 #if defined(OS_WIN)
 #include <windows.h>
 #include <shellapi.h>
 #endif  // defined(OS_WIN)
@@ skipping 1920 matching lines @@
   if (web_contents == tab_strip_model_->GetActiveWebContents())
     window_->SetStarredState(starred);
 }
 
 ///////////////////////////////////////////////////////////////////////////////
 // Browser, ZoomObserver implementation:
 
 void Browser::OnZoomChanged(
     const ui_zoom::ZoomController::ZoomChangedEventData& data) {
   if (data.web_contents == tab_strip_model_->GetActiveWebContents()) {
-    // Only show the zoom bubble for zoom changes in the active window.
-    window_->ZoomChangedForActiveTab(data.can_show_bubble &&
-                                     window_->IsActive());
+    window_->ZoomChangedForActiveTab(data.can_show_bubble);
     // Change the zoom commands state based on the zoom state
     command_controller_->ZoomStateChanged();
   }
 }
 
 ///////////////////////////////////////////////////////////////////////////////
 // Browser, ui::SelectFileDialog::Listener implementation:
 
 void Browser::FileSelected(const base::FilePath& path, int index,
                            void* params) {
@@ skipping 586 matching lines @@
   if (contents && !allow_js_access) {
     contents->web_contents()->GetController().LoadURL(
         target_url,
         content::Referrer(),
         ui::PAGE_TRANSITION_LINK,
         std::string());  // No extra headers.
   }
 
   return contents != NULL;
 }