I agree that the police acted properly in this case. An 11 year old girl should not be severely punished for writing her name in concrete. Her parents should be liable for the damages though.
As a concrete contractor with my own company since '97 and 15 years working for other people before that, I can tell you that most likely the city will not pay to have the sidewalk replaced, they will come back on the contractor and hold them responsible for the damages. (should have protected the work until it was hard enough to be safe), much like the contractor is responsible for protecting the pour from the weather, if its too cold, you put blankets to hold the heat, if its too hot, you put a curing compound to seal the top. if it rains, you cover with plastic to protect it. You don't get paid for damaged work, whether or not it was your fault, it is always your responsibility.
BTW Tucker is right.