[tsimionescu]

This is only part of civil law. Civil law also governs numerous government regulations as well. If you're fined for illegal parking, that happens in a civil court too - but it's still a suit between you and the state. Even in your example of a destroyed fence, the reason you can bring such a suit in court is that there are state or federal laws that I broke by destroying your fence. If such laws didn't exist, a judge would not help you.

What you're thinking more of is contract law - where two parties go before a judge simply to adjudicate a matter that is entirely of their own invention. If we had signed a contract that said I can touch your fence but in touching it I left a hand print on it, I might think the contract allowed me to do so, while you may think that the hand print constitutes wrecking your fence, and we can go before a judge to decide and enforce said decision. The judge then won't look at any state/federal laws, they will look only at the terms of our contract (assuming the contract itself doesn't violate any laws, of course).