It's less a parody of what the book was about and more a parody of Nazi Germany - and showing what great fun and how exciting war is to the kids.
As an Australian, I laughed heartily, and considered it just deserts for that Simpsons episode. ;-)
Verhoeven is something of an expert on this, since he grew up in The Hague during Nazi occupation.
There's an interview out there where he says when he making the film he was wondering if his movie was in-your-face enough about Nazis, to really make sure his movie wasn't too subtle or that people would miss the point he had the former Doogie Howser actor wear a SS officer's trenchcoat.