I believe
the origin is French,
(edit: Slavique Nuke beat me to it) so interesting that it is found in at least three other languages. I wouldn't say it is common usage in English, and the meaning is perhaps not what Staubsauger really intended. Pulling chestnuts out of the fire is about doing something unpleasant or harmful that is to the benefit of somebody else, who doesn't really deserve such a favour (In de la Fontaine's fable, cat burns its paws pulling chestnuts from the fire, but a monkey eats them all).
I suspect that staubsauger might have meant that van Aert might pull the cat out of the bag.
I also suspect that Potomac has a very strange idea of human anatomy.