A very thought-provoking question, and I don't suppose I have an answer.
For a start, I feel that if a crime is in danger of being repeated it should qualify; people who interfere sexually with children are usually repeat offenders.
And then there is a crime where repetition wouldn't be likely to occur (perhaps murdering someone in anger), but the seriousness overcomes being forgiven without legal restitution being made (i.e. probably a lengthy term of imprisonment in this case).
I suppose that if someone drove recklessly while angry and there were no consequences, that need not be reported, especially if they went for therapeutic help on anger management. But if there were consequences like injuring or killing another, again the seriousness ought to take precedence.
If it came to stealing something minor from a shop, undetected, and someone was genuinely remorseful, personally I think that could be dealt with in-house - maybe by making financial restitution anonymously and stripping of "privileges".
No hard and fast rules perhaps, but I suppose the problem would be about leaving such decisions in the hands of people who know the perpetrator personally and who would be biased about bringing a bad name on the organisation.