I'm not exactly sure how important is to save the content as is, rather to allow users to see what I see when I want to share with them something. Sort of advanced page/screen-shot taker with easy sharing of such shots.
Another way to do this would be having a service to rip and rehost content, somewhat similar to a FLV-ripping site (ie. download from Youtube). This kind of site would likely violate copyrights on the rehosted content. You could provide your user/pass to another site, then this service could use your creds to crawl a restricted site and constantly update itself -- but how many people would trust a random crawling site?