Does a plaintiff have to resort to full insurance coverage when the insured has been injured by an uninsured motorist?

Under the statutory scheme, the insured's right to payment matures when the insured has been injured by an uninsured motorist and there is no dispute regarding the liability of the motorist and the extent of damages. "The statutory scheme contemplates that once the uninsured motorist coverage comes into play, the injured insured has resort to the full coverage for which he [or she] has paid." (Kirkley v. State Farm Mut. Ins. Co. (1971) 17 Cal.App.3d 1078, 1082, 95 Cal.Rptr. 427.)