Hoffmann wrote self-serving memoirs that made him look great and got away with it, mostly. We're quite sure, for instance, that his story of Rennenkampf and Samsonov arguing at the train station is incorrect since Rennenkampf was, at the time, confined to a stretcher due to injuries, and nowhere near the train station in question. His personal correspondence at the time doesn't make him look nearly as good, and it casts a lot of doubt on his denunciations of Prittwitz, who admittedly did panic (though we're not exactly sure how much he did in fact panic and how much was Moltke misinterpreting events in a very trying period of time) but was more of a fall guy for the draw at Gumbinnen than anything else. Ludendorff was overly excitable and it certainly wasn't
entirely his plan - hell, it was basically a copy of a plan
Schlieffen had used in a war game a few years before his retirement. And Hindenburg ended up playing the role that commanders usually were supposed to have played in the Imperial German Army - a calming, sane influence that brought everybody back to reality. He didn't get elevated to such an exalted status in national culture just by being a figurehead. There was some truth behind the myth.
To be honest, I'd be hesitant to apply the label of 'hero' to any of the German generals. It really was a team effort, more so than many campaigns, with no overarching 'brilliant mind' sketching the dispositions, while many of the individual German units performed their roles with amazing courage and skill. Everybody made mistakes, everybody had moments of genius or glory, and the adjective that best applies to their performance as a whole is 'professional'.
there's also something to be said about the fact that the Russians announced their marching plans on uncoded radio multiple times.
So did the Germans, but that's an inconvenient truth that can be ignored because the Germans won. Coding and decoding practices at the time often meant that attempting to use the radio in total secrecy for
anybody took longer than was profitable in time-sensitive military operations. And it wasn't that unreasonable of a risk - at the time - for the Russians to suppose that the Germans weren't listening in on that frequency. They got caught quite by chance, and the result of the radio intercepts was mostly to confirm the Germans on a path they were already going down.