The book looks at that document as a sort of smoking gun, too. I think the simplest explanation is that Kulle didn't think the SS thing was a big deal, just a technicality he had to work around to get into the US, and that OPRF (our high school where he worked) didn't really know much about it either. It wasn't unusual for someone to have contemporaneous German documentation --- especially in Chicago, which was a hub for post-war immigration. Gross-Rosen in particular was not well known, even into the 1980s --- the centerpiece of the book is a sort of courtroom drama wherein Kulle's lawyer attempts to convince a judge that there wasn't much of anything untoward about the camp at all.

So the short answer is probably that nobody looked too carefully at Kulle's documentation when he signed on to a low-level janitor's job at a high school.