Yes, if it is determined by their insurance company (possibly determined by the police report) and /or if the person admits they were in the wrong in normal conditions the other insurance company will pay. In some instances your insurance company will subrogate against the other insurance company for the repair costs. If the other insurance company has not accepted liability and you want the repairs to be performed, you may want to go through your own insurance company to expedite repairs. In this case you may owe your deductible until your insurance company settles with the other insurance company. Police reports can take 2-4 weeks to process for use in liability conformation.