you could load a site for browsing using a frame on your own html page, (use PHP/ASP/PERL -or whatever your favorite active language is) to load the content as if it were at the site you were browsing to.
as LK said, this would very much restrict your browsing to just seeing pages, unless you loaded the page and then searched through and modified the links, so it looked like the page was at your own site...
but again you won't be able to use the active content of a site, (well not a site that used post commands...) you could cache GET method pages on your server, but there would be a severe lag, and any site that required a session or cookie to be established, (practically any forum) would be (I think) impossible to re-render on your own site.
to set you on your way...
you could load a plain html page from a 'resticted' site onto your own site simply like this....
All you administrator would see is that you had requested a page from your own site, and the content would not be visible to the administrator...
though practicalyl you'll enjoy this for about five minutes before the administrator looked over your shoulder and banned you for life.