Well, since no one else is taking a shot, I might as well...

Most of what we know about the Nazi high command is the result of Albert Speer's book Inside the Third Reich. Speer was one of the highest-ranking Nazi officials to survive both the war and the Nuremberg trials and, after serving his 20 year sentence, wrote the book. In his portrayal, Hitler's inner circle was most definitely a hotbed of infighting. In his telling, Hitler had erratic work habits and behaviors and refused to properly delegate or define areas of responsibility. As a result, many ministries and departments had overlapping responsibilities and the various leaders had to play "court politics" with each other to get anything done. As an example, Speer found it necessary to align himself with Joseph Goebbels to counter Göring's incompetent economic leadership, during a period that he may well have been targeted for assassination by placing himself in the care of an SS doctor who reported to Himmler. Other examples of the chaos in the inner circle was Rudolf Hess fleeing the Reich by a solo flight to Scotland in 1941 in order to try to negotiate peace with Britain without Hitler's authorization. After the defeats at Stalingrad and El Alamein, Hitler withdrew further and further from reality and his personal secretary, Martin Bormann, took advantage of this and controlled access to Hitler to accrue massive amounts of power for himself. While there are doubts about many parts of Speer's accounts, especially in his complicity in using slave labor and knowledge of the Holocaust, most of what he claims stands up to historical scrutiny.

In addition to Speer's writing, we have examples of literally bloody internal Nazi politics. Most notable is the Night of the Long Knives was an internal purge of the Nazi party that resulted in between 77 and 150 deaths (estimates vary). Wikipedia lists 26 assassination attempts against Hitler, perhaps a third of them by German military personnel. Outside the party proper, the Gestapo regularly executed suspected communists, anarchists, and other political foes inside Germany long before the war began.

So, while literal "advancement by assassination" wasn't commonplace, there was plenty of infighting and a pretty high body count. Given that, it is no real surprise that fiction writers take that as a starting point and then exaggerate it further.