The java applet can get the data from a website other than from where it is downloaded. All you have to do is to have some server program on that web site from where you intend to get the data. The server program will serve the requested data to the applet.
It is like some x party is implementing some server Object with some services and they are specifying the mode of accessing the data rather you should say a mode of calling the services which will serve the data.
Now any one can write their client object (applet) to access the data. Example : Microsoft Outlook Express mail client can login to any mail server (whichever you specify) and can retrieve your mails.