Do you mean you want to access the SOURCE CODE of the "non-local" site? Can you be more specific as to what you want to "copy and paste"?
The IP address resolving that way is not surprising - and without knowing anything about the non-local site topology (network and hardware) you'll need to better explain your objective. The only thing I can think of is you're trying to access the docroot (code) which would required either FTP or SSH access to it from the Internet and the appropriate client on your computer to do so. If so, consult the webhost support to get info on either if its your site or ask the owner to do so if not.
Otherwise if you need to simply copy public visible content on the web site itself, just open a browser window with the URL of the site and copy text or right click "save as" for images, or download inspection and web developer tools for your browser (i.e Firebug, or use Chrome with Web Developer extension) which can get all kinds of useful info about a site to isolate CSS, images, HTML, Javascript and so on for copy/paste on a simple non-dynamic site.
One word of caution:
If the "non-local" site is a PRODUCTION instance, meaning a live web site, it is unwise to change code on it directly without doing so on your local first and then using a repo to commit/push changes that way or FTP or scp via ssh. Your local should be used for development and testing, only move tested/stable code over to the non-local prod instance. Same can be said for content, too.
Hope this helps, if not then please address my questions above and we'll be able to help you better. Cheers.