Can an insurance company deny a defense at a time when it has reason to believe there is potential liability under the policy?

In particular we note the following statement in Mullen v. Glen Falls Ins. Co. (1977) 73 Cal.App.3d 163, 173-174, 140 Cal.Rptr. 605: "[S]tated in another manner, may an insurance company, without making an investigation of any kind, deny an insured a defense at a time when it has reason to believe that there is potential liability under the insurance policy, and then rely upon the results of the personal injury lawsuit and subsequent factors to prove that there was in reality no potential liability in the first instance? ... [p]We believe that public policy alone mandates a negative answer to the question; otherwise an insurance carrier could refuse to defend its insured on the slightest provocation and then resort to hindsight for the justification. Furthermore, a contrary holding would force the insured to finance his own investigation and the defense of the lawsuit, and then to seek reimbursement in a second lawsuit against the insurance company. This, in turn, could not only impose an undue financial burden on persons who have purchased insurance protection, but it could deprive them of the expertise and resources available to insurance carriers in making prompt and competent investigations as to the merits of lawsuits filed against their insureds."