I think I understand. The facts should be told because no one would really take the facts at face value, and not draw any conclusions from them. Using the original example, if they say 'they are going to cut off his head' then whoever hears the message will be allowed to work out for themselves whether or not the 'debt to society' was paid. But if they tell us from the start how to think about the events, then we are prejudiced, or at least an attempt has been made to prejudice us.

In this specific example of prison/execution, we already think that the justice system is fair, and that it would be good and proper to only tell people that a debt has been paid, but in other scenarios, including executions in certain other countries, it would be in the best interests of democracy for only the facts to be told. If the general populace decides that a debt has been paid, then the system works, and if people decide that the punishment was unfair, then the system would be adjusted by public opinion (in a perfect world of course).

The idea 'they are going to lock him away and feed and house him for free for the next ten years' could perhaps be seen as a positive, but only within a vacuum. I think that the kind of person who would see a ten year jail sentence as a positive would not be likely to be swayed by platitudes such as the repayment of a debt to society. If anything, stating the facts may remove some air of romanticism or abstraction from the core concept at hand, and serve as a better deterrent than an allusion to a balance within society. ("If you do this, we will kill you" seems to be a rather powerful motivator to me, at least.)