Make ClearBrowsingDataHandler only observe its own removal task

chrome/browser/resources/settings/clear_browsing_data_dialog/clear_browsing_data_dialog.js

Index: chrome/browser/resources/settings/clear_browsing_data_dialog/clear_browsing_data_dialog.js
diff --git a/chrome/browser/resources/settings/clear_browsing_data_dialog/clear_browsing_data_dialog.js b/chrome/browser/resources/settings/clear_browsing_data_dialog/clear_browsing_data_dialog.js
index efe2b054179524563fdfd0fa37984ee861925025..f4552bc25521bebd9455e60ca3bd9e4317ef3e88 100644
--- a/chrome/browser/resources/settings/clear_browsing_data_dialog/clear_browsing_data_dialog.js
+++ b/chrome/browser/resources/settings/clear_browsing_data_dialog/clear_browsing_data_dialog.js
@@ -65,9 +65,6 @@ Polymer({
   /** @override */
   ready: function() {
     this.$.clearFrom.menuOptions = this.clearFromOptions_;
-    this.addWebUIListener('browsing-data-removing', function(isRemoving) {
-      this.clearingInProgress_ = isRemoving;
-    }.bind(this));
     this.addWebUIListener(
         'browsing-history-pref-changed',
         this.setAllowDeletingHistory_.bind(this));
@@ -84,8 +81,8 @@ Polymer({
     this.browserProxy_ =
         settings.ClearBrowsingDataBrowserProxyImpl.getInstance();
     this.browserProxy_.initialize().then(function(isRemoving) {
-      this.clearingInProgress_ = isRemoving;
       this.$.dialog.showModal();
+      this.clearingInProgress_ = isRemoving;
     }.bind(this));
   },
 
@@ -139,12 +136,15 @@ Polymer({
    * @private
    */
   onClearBrowsingDataTap_: function() {
+    this.clearingInProgress_ = true;
+
     this.browserProxy_.clearBrowsingData().then(
       /**
        * @param {boolean} shouldShowNotice Whether we should show the notice
        *     about other forms of browsing history before closing the dialog.
        */
       function(shouldShowNotice) {
+        this.clearingInProgress_ = false;
         this.showHistoryDeletionDialog_ = shouldShowNotice;
 
         if (!shouldShowNotice)