Quite true and good point to remember... but the source is PBS, after all.
Saddam was in control of the intelligence apparatus at that time and had managed to get managerial control over Iraqi oil, and though not the official head of state as PBS implied, he certainly had Iraq by the short hairs. He didn't become 'absolute' ruler until 1979 when al Bakr resigned and Hussein wasted half his own cabinet officials and a bunch of his potential Baathist rivals.