No, you're not doing anything wrong

Some background:
The version of Celestia that Don used (v1.4, I suspect) placed the observer at a fixed position relative to Celestia's "universal coordinate system". If you look at the distance value shown in the top left of Celestia's window, you'll see that the viewpoint is 206 AU away from the selected object. Celestia originally had its origin (the position where coordinates are [0,0,0] ) some 200 AU away from the Sun to avoid numeric problems often seen when one is working with very tiny values. Celestia's algorithms have changed since then, so that's no longer a problem. In order for Celestia to be able to work correctly with the ephemerides used by NASA, Celestia's origin is now at the Solar System's barycenter, the position in space around which the Sun and all the planets orbit. For the same reason, Celestia's internal time scale has changed.
It used to be that when Celestia drew spacecraft orbiting distant planets (like Cassini around Saturn), they'd be drawn hundreds of kilometers away from where they were supposed to be, often colliding with the moons. Now they flyby moons almost exactly where and when NASA's official publications say they should. There are some minor differences which usually can be attributed to NASA using slightly improved spacecraft orbital parameters which have not yet been published.
In addition to these coordinate system changes, the format of URLs seems likely to change, too. The URLs generated by Celestia v1.6 and later contain a version number at the end, so there's some hope that some compatibility can be maintained with future versions.