I think a good solution to this problem might be to examine the magnitude of the question. In the case of the bank robbery it can be observed that the crime is an individual transgression that left little to no impact on anyone. Most banks are relatively unaffected by a single robbery and the individuals involved are given counseling and medical help as is neccessary; its a fairly rountine hazard of working in a bank, just like the odd hold up can be expected at a convenience store. It is likely that the educated children in question will feel guilt, but together they are in a position to make restitution for this evil in their pasts if they feel that it is neccessary. If this is the case it can definately be put forth that good has come from this robbery.

Now, consider the other case, where the government is trying to apologise for centuries of theft and rape (in every conceivable sense of the word) with a few tax dollars. What good has come of that? Tax dollars are not enough in this case, almost anyone who were to do a somewhat detailed study of history would agree. A sense of justice balks at the injustices that have occured, a pacifist would be sick with rage. 'Might makes right' and the broken philosophical ideas that people tried to build up around the evolutionary theory (which, for the most part, would likely have made Darwin scream) are the only possible ways of justifying this, and they are discredited by almost any philosopher who actually studied philosophy.

Of course, this all falls under moral relativism of the worst sort, so some may sway to one side or the other of my argument, saying that restitution is needs in both or neither case. It's all a matter of taste.

Anyway, that's my bit, have at it.