You are absolutely right, but that is the job of the board of directors. If the board is doing their job, and admittedly many do not, they are making sure the executives aren't putting their interests before the interests of the shareholders.
If any two business theories are true they are the Peter Principle and the Principal-agent problem. Too many boards don't take care of the later but in the end paying executives less wouldn't decrease price, there is no logical economic reason to do so, especially in the oil industry. They would charge the same and instead of paying the executives they would invest the funds in a way that benefited the shareholders (either with dividends or capital expenditure aimed at future revenue). The most important factor to setting price is demand. All lowering executive pay would do is change how the profits are distributed after they are made, they wouldn't lower the profits.