I hear that a lot, and at least in CA (and I suspect most/all other states) a police report is NOT required to make a claim. Some insurance companies seem to think the police take these reports, but there are many collisions that we do NOT take.
A non-injury collision does not require a collision report by the police in CA ... if we took every small fender bender and dent that occurred, we'd have to hire additional officers just to take collision reports so we could provide the information to insurance companies. Collisions are generally NOT a law enforcement issue, they are civil, and they are very often a huge drain on available resources.
Some agencies will take collision reports without injuries, and some will even take them late ... but those are generally a policy issue and not a legal one. In CA a counter report or a late report can NOT include a determination of fault, so it does not do much more good than to gather the information for the insurance company - which is precisely what they want so they won't have to.
- Carl