"Abd al-Hadi, whose full name is Nashwan Abdulrazaq Abdulbaqi, was born in 1961 in the Kurdish city of Mosul, northern Iraq. He did national service in Saddam Hussein’s Army, rising to the rank of major, but left for Afghanistan in the mid-1980s to join the jihad against the Soviet Union.

Another Time Online article.

The mid-1980s...the discredited old lie about a connection between Iraq and al-Qaeda is still a lie and remains discredited. "

I fail to see how this proves your point.
How does someone in Saddam Hussein's army rise to rank of major?
Keep a few things mind, Iraq is now and then a tribal society- you should not think of Abd al-Hadi as merely an individual.
And the Iraq army is not the American army- where some farm boy with no family connections can rise through the ranks by education and merit.

Next, you need to ask what options a Iraqi army major has as far leaving the country of Iraq. Most Iraqis who leave Iraq do so illegally- but this doesn't mean that this Major did this. It seems more likely in this case that the Iraqi state approved of his departure.
Keep in mind that the Iraq-Iran occurred between "September 1980 to August 1988"
http://en.wikipedia.org/wiki/Iran-Iraq_War

Why would the Iraqi state allow one of it's majors to leave the country in the middle of a war- a very serious war, one that threaten Iraq's existence?
If the assumption is that this major left the country without the approval of the state, how does his tribe explain why one it's member is not available to fight against the immediate and mortal threat of Iran? Not only that but Major apparently remains in good standing and is able to return to Iraq without being executed for abandoning his nation in time of great need of his leadership and participation.

Instead [according to the source you quote] it seems very likely that Saddam involvement with al-Qaeda begins quite early and the involvement is quite deep- in that, the formation of al-Qaeda may have been greatly influenced by Saddam.