State laws differ but in general the insurer also has the responsibility to determine which driver is at fault in an accident. This typically means that an insurance adjuster does have the right to disagree with a police report and determine fault in a different manner. Sometimes an adjuster will split up fault differently than the police or determine fault to be placed on a different person then what the police report states.
An adjuster's investigation and determination of the claim usually takes into account both drivers' recollection of the accident and the damage of both vehicles. Many times a claims adjuster's findings will agree with the accident report but there are times when it does not and they assign blame differently then the police. To find out what your state insurance laws say about this situation you can contact your state's insurance regulatory body.