I will offer what I took the scenario to be, and why I gave the answer that I did. Bob can comment if I misinterpreted the scenario.
In my interpretation, the pseudo-FDR had multiple motives. His first and primary motive was to further the war effort. However, the means to that end involved covering up a murder. (In the hypothetical, he was also actually the murderer, but the question only involved obstruction of justice, so the fact that he, personally, was the murderer is not all that relevant.) So, in furtherance of the cause of victory, he decided to quash the murder investigation.
Quashing the murder investigation, though, was still part of the crime of obstruction of justice. The question for the prosecutors and the jury would be whether his overall motive, helping win the war, justified the actions. Regardless, deliberately covering up the crime constitutes a "corrupt intent". At least, I think it does. I'm not going to go back and read the statute and cases for the exact wording to see if the "corrupt intent" is cancelled if it is the means to a non-corrupt end. I think that the statute's wording was such that deliberately covering up a crime is automatically considered corrupt, for the purposes of that law. If anyone who is willing to look up the actual statutes and court precedents were to present them, I would read the quotes and analysis.