The police only show up to record what the parties involved tell them. It IS important to get a police report, as it can help you determine who is closer to the truth when there are conflicting statements, but that is about the extent of the usefulness of the report. Just a record of observable facts of the accident, after the accident happened. Locations of vehicles, skid marks, damage on vehicles, etc. The police weren't there, so they don't know any more than the adjuster does. Plus, the police are only dealing with criminal issues. Insurance is a civil matter. I had many claims where people would say to me "Well the other guy got the ticket, so he must be at fault." or "Well the officer said the other person was at fault."
I have to explain to them that it doesn't really matter what the police said, as they don't get to decide the civil matter in this case. Asking a police officer for accident advice is about as much of a poop shoot as asking about gun laws. Police have a LOT of laws and regulations to be aware of and they really can't be experts on everything.
So, a police report can be a great thing to have, but it can also be completely meaningless. With that said, I fully agree that in ANY accident, it is always the best idea to call the police and try to get a police report. This will prevent people from completely denying involvement in an auto accident. It sounds ridiculous, but people do that all the time. Car accidents suck.
EDIT: I really hope I'm not coming across rude, as I'm not trying to be. It's just that the police aren't in charge of deciding fault in auto accidents. They write down what people tell them, record any facts that are available, and that's it.