When the British analyzed the German Enigma Code, they were able to intercept the daily reports given by the camps. Total number of people in the camps, people in, people out, number of deaths and cause of death were reported. By far the biggest cause of death reported was disease but they also mentioned shootings and executions. What was never mentioned is what always gets sold out as the main cause of death; gassing. To quote from Francis H. Hinsley - British Intelligence in the Second World War:

“The messages from Auschwitz, the largest camp, with 20,000 inmates, mention disease as the chief cause of death, but also include references to executions by hanging and shooting. The decoded messages contain no references to gassings.”