"base" URI may consist of host+port+path not _just_ host or host+port. you don't have to switch subdomains or hosts in order to provide RESTful interfaces.
But the git web UI doesn't have a path component. As far as I can tell, it's always just '/' with a huge querystring on the end.
it's a client to the restful interface... web browsers current suck at restful interfaces because forms don't support all the http methods, and you can use your own image for a button (or other form element).