PDFs viewed inside a <webview> should navigate the same as PDFs in tabs.

chrome/browser/resources/pdf/pdf.js

 // Copyright 2013 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.
 
 'use strict';
 
 /**
  * @return {number} Width of a scrollbar in pixels
  */
 function getScrollbarWidth() {
@@ skipping 23 matching lines @@
     return decodeURIComponent(filename);
   } catch (e) {
     if (e instanceof URIError)
       return filename;
     throw e;
   }
 }
 
 /**
  * Called when navigation happens in the current tab.
+ * @param {boolean} isInTab Indicates if the PDF viewer is displayed in a tab.
  * @param {string} url The url to be opened in the current tab.
  */
-function onNavigateInCurrentTab(url) {
-  // Prefer the tabs API because it can navigate from one file:// URL to
-  // another.
-  if (chrome.tabs)
+function onNavigateInCurrentTab(isInTab, url) {
+  // When the PDFviewer is inside a browser tab, prefer the tabs API because
+  // it can navigate from one file:// URL to another.
+  if (chrome.tabs && isInTab)
     chrome.tabs.update({url: url});
   else
     window.location.href = url;
 }
 
 /**
  * Called when navigation happens in the new tab.
  * @param {string} url The url to be opened in the new tab.
  */
 function onNavigateInNewTab(url) {
@@ skipping 190 matching lines @@
       this.zoomManager_.onBrowserZoomChange.bind(this.zoomManager_));
 
   // Setup the keyboard event listener.
   document.addEventListener('keydown', this.handleKeyEvent_.bind(this));
   document.addEventListener('mousemove', this.handleMouseEvent_.bind(this));
   document.addEventListener('mouseout', this.handleMouseEvent_.bind(this));
 
   // Parse open pdf parameters.
   this.paramsParser_ =
       new OpenPDFParamsParser(this.getNamedDestination_.bind(this));
+  var isInTab = this.browserApi_.getStreamInfo().tabId != -1;
   this.navigator_ = new Navigator(this.browserApi_.getStreamInfo().originalUrl,
                                   this.viewport_, this.paramsParser_,
-                                  onNavigateInCurrentTab, onNavigateInNewTab);
+                                  onNavigateInCurrentTab.bind(undefined,
+                                                              isInTab),

[Dan Beam, 2015/09/29 22:38:26]

function() { onNavigateInCurrentTab(isInTab); },

[Dan Beam, 2015/09/29 22:38:58]

function(url) { onNavigateInCurrentTab(isInTab, url); },

**

+                                  onNavigateInNewTab);
   this.viewportScroller_ =
       new ViewportScroller(this.viewport_, this.plugin_, window);
 
   // Request translated strings.
   if (!this.isPrintPreview_)
     chrome.resourcesPrivate.getStrings('pdf', this.handleStrings_.bind(this));
 }
 
 PDFViewer.prototype = {
   /**
@@ skipping 653 matching lines @@
    * Each bookmark is an Object containing a:
    * - title
    * - page (optional)
    * - array of children (themselves bookmarks)
    * @type {Array} the top-level bookmarks of the PDF.
    */
   get bookmarks() {
     return this.bookmarks_;
   }
 };