The issue here is not that the kid shot and broke you basketball backboard. The issue here is the kid's lack of respect for authority. I couldn't care less if we were outside and all shooting and he accidentally shot and brake something. Ish happens. Where the issue comes in, is the fact that the kid blatantly defied direction given by an adult, the parent of a friend, and the owner of the property he was on. I would hope you would do this kid the justice of taeching him there are consequences for not following the rules. By not doing anything, you are teaching the kid he doesn't have to abide by the rules set forth by the governing authority, in this case, you. Is that what this society needs? Even more kids with no regard for anyone or anything else because they have never had to take responsibility for their retarted decisions?
If I was this kid's parents, I would WANT you to tell me what he did so I could discipline him myself. If the parents can't afford to pay for the damages, that would be no big deal to me. If you feel gracious enough to not request that of them because you are aware of their financial situation, by all means, extend that grace. That is secondary though. Most importantly, they need to be made aware of what he did so they can deal with it accordingly. Otherwise this kid is going to grow up to be a pirate.