Firefox document object lacks DOM properties in XSLT-generated pages

I started working on a keyboard-shortcut library and knew (somewhere in the hidden inaccessible depths of my mind) that I had a problem with document.body property a while ago. As it's required by the HTML DOM standard, I immediately suspected that it was an IE problem ... and chased that ghost for a while, until I've realized how wrong I was.

The buggy browser was Firefox: if you create a web page with local XSLT transformation (dictated by the xml-stylesheet instruction in the XML document returned from the server) in Firefox (up to at least 2.0.0.6), everything looks normal, but document.body is null and document.forms, document.links and other similar array are empty.

To make matters more confusing, all other HTML DOM calls work (it's a different bug from this one), so I had to substitute the links array with document.getElementsByTagName("A") and the body property with the document.getElementsById("body") (and used the id attribute on the body tag).