My dad told me if your kid only understands 1/10th of what you're telling them then you only have to tell them ten times, or a hundred times, or whatever.  Don't take it to heart that your 9 year old questions his responsibility even though you've already told him.  If you want to get all fancy the apology letter can include his side of the story, why he did it, then add what's at least one thing he's changed his mind about since making that decision last time.  (dishonest? don't learn as much? lost credibility?  Or the other direction: I need to take it easier on myself to try hard and make honest mistakes.  I've learned that's part of the learning process.)
I've been reading this comedy website called cracked.  I just read a piece called

"6 types of apologies that aren't apologies at all"
"I deeply regret " means I'm sad it happened without taking responsibility.  (end it with "if I've let you down).
"mistakes were made" (was there even a culprit?)
"I think you misunderstood what I was saying and for that I apologize"
(a passive aggressive way to shame anyone you offended)

And I just got this off of FB:  "saying I'm sorry doesn't always mean you're wrong.  Sometimes it just means you care about the other persons feelings and your relationship is more important than your ego."

Just some recent thoughts I've read regarding apologies.  Don't read too much into it that your kid doesn't see this situation the same as you do.  You have a lot more years of context clues giving you a lot more meaning on how his choices have affected him and other people including you.  

There's a lot of rambling mish-mash in this post so now I feel the need to apologize for the bad formatting and not putting forth the effort to edit it pretty for form or content.


Youth lives by personality, age lives by calculation. -- Aristotle on a calendar