Relanding this with fixes for the unit test failures which required addition of some more plumbing …

ui/views/controls/webview/webview.cc

Index: ui/views/controls/webview/webview.cc
diff --git a/ui/views/controls/webview/webview.cc b/ui/views/controls/webview/webview.cc
index 3e07f6f42322810d6eeceb809167c672b579d282..e7885005272b60c12fd514ee434102bb64d7c9ba 100644
--- a/ui/views/controls/webview/webview.cc
+++ b/ui/views/controls/webview/webview.cc
@@ -13,6 +13,7 @@
 #include "ipc/ipc_message.h"
 #include "ui/accessibility/ax_enums.h"
 #include "ui/accessibility/ax_view_state.h"
+#include "ui/aura/window.h"
 #include "ui/base/ui_base_switches_util.h"
 #include "ui/events/event.h"
 #include "ui/views/accessibility/native_view_accessibility.h"
@@ -301,6 +302,12 @@ void WebView::AttachWebContents() {
   OnBoundsChanged(bounds());
   if (holder_->native_view() == view_to_attach)
     return;
+
+  // Fullscreen widgets are not parented by a WebContentsView. Their visibility
+  // is controlled by content i.e. (RenderWidgetHost)
+  if (!is_embedding_fullscreen_widget_)
+    view_to_attach->Show();
+
   holder_->Attach(view_to_attach);
 
   // The view will not be focused automatically when it is attached, so we need
@@ -320,6 +327,11 @@ void WebView::AttachWebContents() {
 
 void WebView::DetachWebContents() {
   if (web_contents()) {
+    // Fullscreen widgets are not parented by a WebContentsView. Their
+    // visibility is controlled by content i.e. (RenderWidgetHost).
+    if (!is_embedding_fullscreen_widget_)
+      web_contents()->GetNativeView()->Hide();
+
     holder_->Detach();
 #if defined(OS_WIN)
     if (!is_embedding_fullscreen_widget_)