Entire 'Great Escape' Sequence Invented
The entire "Great Escape" sequence appears to be a fabrication, not by RSM Charles Coward, but by the producers of the movie. It borrows heavily from real events that occurred at a POW camp different form the one where RSM Coward was actually interred.
I haven't read COward's own claims, but the references I find about him online make no claims about being involved in a mass break out of Allied POWs. "The Great Escape" took place at Stalag Luft III outside Sagan, then in Germany (Silesia) and after the war in Poland. RSM Coward had been transferred from Stalag Luft III to Stalag VIII B several months before the escape was made. In fact, he was at the Work Camp in Auschwitz when the escape occurred.
So far as I have been able to find so far, RSM Coward makes no claim that he was involved at all with "The Great Escape." He does say all along that he was in Stalag VIII B. I think the entire POW camp sequence was invented by the movie's production team borrowing heavily from the true exploits of British and Canadian officer POWs in Stalag Luft III.
During the time frame the RSM Coward is depicted as aiding to an escape that happened at a camp where he was not resident, he was actually saving Jewish internees from certain death at Auschwitz. I don't know why the producers chose to invent material while down-playing RSM Coward's true accomplishments, but that is how it looks.
BY the way, there were some American POWs in that camp and a few of them helped with the tunnels. A couple have even said that they were on the list to take part in the escape. However, all American POWs were transferred to Stalag Luft VIII B (a sub-section of Stalag VIIIB) established in the Fall of 1943. This was done to reduce over-crowding at Stalag Luft III. As has been discussed in various threads of the on the board for "The Great Escape," that movie is also heavily fabricated to invent more roles for American characters, hence more American box office stars. At least that fabrication can be clearly seen to be about money.