It made a largely circumstantial case for IBM's involvement in the holocaust.
Yes - the following things are true:
* Germany used IBM Tabulating Equipment to compile its racial census.
* Deutsch Reichsbahn used IBM Punched Card equipment to run most of its operations.
* The German Government made extensive use of IBM Punched Card equipment to track prisoners, including in the concentration camps.
Beyond those three facts the case is basically circumstantial - Black made a bunch of suppositions when drawing his conclusions -
* IBM New York knew all of the particulars of use of its tabulating equipment, and what the outcomes would be.
* IBM New York had defacto continuing control of its german subsidiary (Dehomag) even after it was functionally nationalized.
* IBM New York provided technology and parts thru IBM Geneva.
* Profits from Dehomag were funneled thru IBM Geneva to IBM New York.
* Most glaringly, he asserts that IBM Punched Card technologies were the only way to do what Nazi Germany did at the scale it did it at.
However he makes the assertions without much backing evidence for it, and its all clouded in an aura of leading purple prose.
This article presents a pretty concise version of the gaping flaws in the book - https://muse.jhu.edu/article/33853
Most notably, the book leaves out important context - even if everything he supposed about IBM were true, what IBM did wasn't unique, it was common corporate practices at the time, indeed, many american corporations had similar subsidiaries, all of whom at a minimum contributed to the german war effort.