Does an insurer have a right to control defense and settlement of the third party action against its insured?

"Generally, an insurer owing a duty to defend an insured, arising because there exists a potential for liability under the policy, has the right to control defense and settlement of the third party action against its insured, and is ... a direct participant in the litigation. [Citations.] The insurer typically hires defense counsel who represents the interests of both the insurer and the insured." ( Long v. Century Indemnity Co . (2008) 163 Cal.App.4th 1460, 1468, 78 Cal.Rptr.3d 483.)