You are correct! I've watched the History Channel's Saddam biography twice in the past week, so I must be an expert by now. ;^) Here's a brief synopsis of the more interesting points:
Saddam's first job in government was as an assassin, trying to topple his own government. The kill fails, but when the government does change hands, he's the #2 man in Iraq. In the Iran/Iraq war, we were providing Saddam with intelligence from satellites, weapons, and advisors when it looked like Iran overwhelming numbers would make the difference in the war. (Oddly enough, at one point in that war, we were providing intel to BOTH sides!) Once he won, the Kurds in the North and the Sunnis in the South tried to take advantage of the weak post-war military... and paid dearly. Saddam just got his chemical WMD's, and had fun trying them out on the rebel villages, since they worked so well on the advancing lines of Iranians. (The images of the bodies of mothers and children fallen in the town streets were very troubling.)
They also had his only American-educated nuclear physicist to interview extensively, with amazing details about Saddam's intense demands to get one working nuclear device at any cost (to quickly and effectively end the Iran-Iraq war). He expertly uses fear as a tool to deal with both his supporters and his opponents. He knows that once he's out of power, his life is worthless, and will take as many people down with him as he can.