First off BP has an overriding obligation to its stockholders. Second, BP has a PR playbook for this scenario that is based upon decades of experience. For the moment BP's money is making the rules.
[ You also fail to mention that many BP employees as well as executives and board members probably have stock options, meaning that they are also looking after their own interests in this matter too. It's not like they want to be altruistic, but these pesky investors are holding them back. And it's not like these 'stockholders' are some external entity to the company with a hard line between investors and employees with no grey area in between. ]
{edit} AIG also had an obligation to their investors to keep the stock price up and up and up... until it came crashing down. Saying, 'they have an obligation to their investors,' is really just a cop out. It's a way of pushing responsibility away (i.e. "Don't blame me! I have a responsibility to the investors, my hands are tied! I'm compelled to this course of action.").