WellPoint Inc. Chief Executive Angela Braly encounters her largest test yet as the nation's biggest health insurer lands under fire for its plans to raise rates as much as 39% in California.

However, Ms. Braly has combated and instead of issuing a Toyota-style apology, she is transforming her critics' argument around, seeking rising health-care costs triggered by doctors and hospitals, which she claims aren't addressed by the current health-overhaul bills.

While, state officials and lawmakers are fueling concerns about its rate hikes in Maine, Connecticut and Colorado, as well as California, as the company's challenges stretch beyond Washington— her strategy is playing well with investors.

Wellpoint's shares had registered a fall when news of the rate increases emerged, however, the stock grabbed almost 2% on the day Ms. Braly testified in Congress, and it is up 115% from the low it hit last March.

Investors reveal that they are relieved that the company is standing by the rise. Without them, Ms. Braly argues, the company can't break even in the risky business of selling insurance to individuals, which has become more difficult as the economy has caused healthier people to forgo buying the policies.