No Mexican president can privatise the oil industry; he simply hasn't the power to do so. PEMEX is and will be a state monopoly until the Mexican Constitution is changed.
PEMEX is 1/5 the size of EXXON but has 3 times more employees. At the very least PEMEX is a very large patronage plum and may be a phantom employee salary producing machine. 50,000, or so, pay checks/month makes for a comfortable retirement.