Well, after reading Judge Bertina Lampkin's dissent along with Judges Thomas Hoffman and Shelvin Louise Marie Hall's majority opinion, I think I've reversed my opinion here... Just reading the statute wasn't really enough, without getting some of the details of the circumstances to this case, and I find myself agreeing with Lampkin. The precedent is on Emanuel's side.
Your reading matches what most of the pundits here have been saying. However, the judiciary in IL can be quite political at times - they are elected by party and often slated by party bosses.
In this case, it's worth noting that one very prominent Chicago alderman is backing a candidate other than Rahm. That alderman also has had a very active role in slating judges over the last few decades. That same alderman's wife currently sits on the IL Supreme Court. Not that this means anything ...