The following code works just fine without FriendlyUrls turned on for an ASP.Net Web Forms project:
So, ultimately I got the solution to my question by making following changes to my project:
Add FriednlyUrls to the project.
Remove the line in RegisterRoutes method that sets settings.AutoRedirectMode
property in App_Start/RouteConfig.cs
(note that setting it to RedirectMode.Permanent or RedirectMode.Off did NOT work for me)
Add authorization in web.config as follows under system.web section
Modify the url in ajax call set up to use Microsoft.AspNet.FriendlyUrls.Resolve function in order to get the correct url as below: