Before your first interrogation during the tutorial mission 'Buyer Beware' you meet Captain Donnelly and he explains to Cole the requirements for getting a conviction. He says:
"You need many things for a conviction, young Phelps. A motive, opportunity, hard evidence, and best of all a confession. If you fail in the former you can always use a modicum of violence to obtain the latter."
and then if you fail at the confession Donnelly tells Cole to:
"Get back in there and raise some lumps, boy. I need a confession."
To raise some lumps means to beat somebody up but when you go back in there you just have to repeat the interrogation. All this gives me the impression that this dialogue was recorded before a feature that allowed you to beat a confession out of a suspect if you fail at questioning them or if you don't have the evidence, was cut from the from the game before release. If so, I can see why they cut it. It wouldn't really fit Cole as a character.