How to download a file from the special folder of a web app using jQuery?

How to download a file from the special folder of a web app using jQuery?

I've had nothing but trouble trying to download a file using simple HTML5, as is evidenced here on StackOverflow

It "sort of" works, but it seems unable or unwilling to identify the "App_Data" folder and its contents.

So, as I wonder aloud in Update 10 on that mega-post:

Maybe what I really need to do is, instead of the simple html, add some jQuery that will download the file. But the question is, can jQuery access the App_Data folder any better than raw/simple html can?

Is jQuery capable of downloading a file from a Web API app's App_Data folder to a user's file system from a web page? If the answer is "yes" do any of you have an example of how?