Looks like when the ISP set the client up, they set the domain info in their own DNS servers. They probably assumed that the client had already registered the domain and pointed it to their nameservers.
They are probably too lazy to change their DNS server entries, especially since many ISP's don't have fancy control panels to manage everything, so they are managed by hand & config files. All they need to do is delete the entry from their DNS configs, and their dns server will properly search/route the domain (just like it does for domains like google and yahoo).
You don't need to view the domain via proxy, the only reason your computer brings up the ISP's server for the clients domain is because you are using your ISP's DNS server. If you go to your network settings, edit your tcp/ip settings and manually set your DNS servers to match your hosts name servers, or any other public nameservers (126.96.36.199 and 188.8.131.52 work well) and you will be able to browse normally.
I've always wondered what would prevent a malicious system administrator to transparently "phish" for info. All it would take is to update the ISP nameservers to route www.paypal.com
to their own webserver, and there would be no way to detect it is a phishing site. Because customers on their network would type in "ping www.paypal.com" and it would resolve to the ISP's server IP directly. Just like your clients domain resolves to the ISP's server, instead of the server the site currently sits on.
And I know plenty of shady people that worked for ISP's. People who have been arrested by the FBI for hacking (actually hacking and taking down networks). One individual actually set up a filter to be able to read AIM conversations that were going on through his (the ISP's) network.