Portions of this film were based on the fourth patrol of the USS Growler and its captain, Lt. Commander Howard Gilmore, who was awarded the Congressional Medal of Honor posthumously. Here are a couple of links that explain more:
http://en.wikipedia.org/wiki/Operation_Pacific
http://en.wikipedia.org/wiki/USS_Growler_(SS-215)
Surprised to read that the submarine ramming incident was based on a true event too, though I somehow doubt it was in the same circumstances as the movie.
In the film the sub had already appeared to (have won an unlikely fire fight with the disguised freighter, even though it appeared to well out gun the sub. It must have been all those sub crewman on board firing sub-machine guns from a long way away that did the trick.
Any way, with the boat burning and disabled, the Duke decides to ram it and in doing so threaten the safety of his own craft and crew.
Why? I'm not sure, but knowing the Duke, he probably had good reasons.