The documentary is not accurate. It's just repeating an assertion from a German economic historian (Rainer Karlsch) who wrote a book over a decade ago (Hitlers Bombe) that no serious historians think is correct. The technical assertions in the book make no sense (and contradict themselves; Karlsch seems to be unsure of what he's actually arguing, and seemingly doesn't understand the science well enough to realize that), and the evidence is exceedingly flimsy given the magnitude of contradicting evidence. It's bad history. There's a reason nobody has bothered translating it into English. I discuss Karlsch's argument in this article, along with the problems. Karlsch is not a hack, but he's clearly not correct on this point. Every piece of serious, hard evidence points to the Nazis being very far away from a bomb. It would take a lot more evidence than Karlsch has to be convincing on a contrary point.

(Karlsch's only "smoking gun" evidence includes: a) Soviet intelligence reports that claim some Germans told them otherwise, which even the Soviet scientists discounted, b) a few scattered supposed eye-witness reports that are not credible, and c), perhaps my favorite leap of interpretation, an account from the USSR that says a Chinese delegation was shown a nuclear test film prior to the Soviet bomb being developed, but claims isn't an American test, so maybe it's captured film of a German test? Hmm hmm. All of this is quite paltry stuff compared to the weight of contrary evidence, which includes quite detailed accounts of what the German scientists were actually doing.)

It is frustrating, as you can imagine, for a serious historian to constantly see bad history about the Nazi atomic project (which did exist but did not develop weapons — they almost developed a prototype reactor, and that is very easy to document), including in what purport to be serious documentaries. Having been interviewed and helped develop several documentaries, I can tell you this: the accuracy of a documentary will entirely depend on what story the director and producer want to tell, and how much they actually care about the accuracy. For most popular, mass-market television documentaries (e.g. History Channel, Discovery Network, whatever), the producer reads a book and says, "ah ha, I know what story to tell!" and then works from that premise. They interview experts only to provide talking heads, to fill out the story they already want to tell. They edit it so it looks like it is a smooth story that everyone agrees on. At best it is a story that is 10-15 years old (because the producer is not on the front-lines of this or reading the latest work on it), at worst it is something that is definitely wrong.

It is a dispiriting process to say the least, especially when you find your own "interview" having been edited in a way that supports a narrative you think is incorrect. I now only tend to work with groups who don't do it this way, whose relationship with the experts is more dynamic (they're not just looking for a sound byte, but understanding). There are groups who do good documentaries on this subject but they are few and far between and, in my experience, often not in the USA, where the demands for hyperbolic and sensational content seem to crowd out all other considerations.