It does not seem that there is a way to pass the original URL as the system identifier of the doc while passing the document as a string or a local file to S::P::O at the moment, or I couldn't figure out how to do it.  The URL storage engine doesn't like /path/to/doc nor file:///path/to/doc, and the OSFILE/OSFD storage engines don't seem to like HTTP "base"s.  I tried things like

$p->parse("<URL base='http://example.com'>/path/to/file");
$p->parse("<URL base='http://example.com'>file:///path/to/file");
$p->parse("<OSFILE base='http://example.com'>/path/to/file");

...but couldn't get it to work.