One difference is that when you visit/bookmark some normal webpage, you save on your computer only its title and address. With this, you are saving the page content as well, just by visiting the page.
Even if this were possible (which, even if tinyurl supported it, would break most browsers) you would be effectively hosting your content on tinyurl.com. Again, this is no different from hosting the file on any of a zillion public data hosting services.