But then when he left his sickbed, got back on his bike and won the Tour de France, the toughest cycling contest in the world, not once, but three times, no one would argue with the word.
He was a miracle man. And he simply won't stop flirting with death.
Just before 60 Minutes II rebroadcast its original story about Armstrong in May 2000, he crashed head first into a wall while plummeting down the Pyrenees. To put it bluntly, Lance Armstrong is lucky to be alive.
About five years ago, Armstrong was America's best cyclist and wasn't terribly modest about it. He was brash. He was invincible.
Then one day he didn't feel so good. He had severe headaches, blurry vision and was coughing up blood. One testicle puffed up to the size of a good-sized lemon, he says. Armstrong finally went to see a doctor in his hometown of Austin, Texas. The doctor wanted an X-ray of his chest.
The doctor found out that Armstrong had testicular cancer, which had spread. It was as bad as this kind of cancer can get. The lungs that would later carry him to three major victories were riddled with tumors - 12 of them. The cancer had spread to his abdomen and brain.
The testicle was removed. And soon the brain tumors had to be as well. His doctors at Indiana University Hospital thought his chances for survival were substantially less than 50 percent. But they didn't tell Armstrong.
"When I was visiting Lance before he was going to have his brain surgery, there was a point that I thought I might be going to Lance's funeral," said Chris Carmichael, Armstrong's coah.
Doctors operated for hours on Armstrong's brain. Then he underwent four grueling cycles of chemotherapy.
"Whatever I do in cycling, or whatever I do in the Tour de France, or whatever I do in training, I'll never suffer like I did then," Armstrong said.
The chemotherapy was administered in cycles: one week on, two weeks off.
So what did Armstrong do when he wasn't feeling nauseous, when he could get out of bed? He rode his bike.
"One day we're out riding on this pretty good hill," Armstrong remembered. "And a lady came up on me. She must have been in her 40s, maybe early 50s, not a very nice bike, right past me, Voom! And I thought, 'This is not happening.' Gave it a little effort, a little surge to try (to) stay with her. Couldn't catch her."
Like every professional cyclist, Armstrong belonged to a team. His was based in France. When Armstrong was in his last phase of chemotherapy, his lowest point, the team managers came to his hospital room.
They were there to cheer him up, Armstrong thought. Instead they had come to cut his salary by 80 percent. Soon he was dropped from the team.
But in December 1996, test results showed Armstrong's cancer was in remission. He said that he is alive because of "good doctors, good medicine, good technology. Twenty years ago, I would've been dead."
By 1997, Armstrong thought he was ready to race. He contacted several teams about becoming a rider for the Tour de France but got no offers. No one wanted a cancer survivor.
Finally, in 1999, a new team sponsored by the U.S. Postal Service took a chance. After a few fits and starts, Armstrong began to train toward the Tour de France, which involves 2,300 miles during 23 days and is one of the most punishing sporting events in the world. He had only completed the race once before, placing 36th. Few thought he could be a contender.
"I didn't have anything else to lose," he said. "That was the beautiful thing."
Armstrong trained as he had never before. Ironically, the cancer had changed his body in ways that weren't all bad. He was 15 pounds lighter, which makes a big difference when riding uphill. In the first stage of the 1999 Tour, he beat his rivals in a race against the clock.
Ten days later, Armstrong was still leading the race. The next stage took riders into the mountains to the alpine village of Sestriere. Armstrong's rivals assumed he would crack.
Five hours of racing later, Armstrong was still climbing toward Sestriere. But two racers had broken away from the pack. They figured they had dropped Armstrong, perhaps for good. They were wrong. Armstrong attacked while going uphill.
Armstrong passed the two riders and kept going. No one caught him. After six hours of riding and 133 miles in the Alps, Armstrong was already an icon.
The French press was convinced that Armstrong had been doped and that the cancer had been faked. When Armstrong passed daily drug tess, the controversy was laid to rest.
As he mounted the champion's podium on the Champs d'Elysees, he knew his victory meant something to people who had never cared about the Tour de France.
"I knew that there were people just diagnosed, or family members or people diagnosed, or survivors or people being treated," Armstrong said. "They were going to see that and say, 'That guy's one of us.' And they were going to get hope from that."
Since first winning the Tour de France, Armstrong has used his fame to spread his message of hope.
Every spring, Armstrong holds a cycling benefit in Austin. Thousands of riders, many of them new riders, cycle to raise money for the fight against cancer. This year's tally was $1.5 million.
He has set up a cancer foundation in his name that has resulted in additional pledges of $10 million. Armstrong has also launched a cancer awareness campaign called the Cycle of Hope.
The miracles didn't stop in France. Before his surgery, Armstrong stored some of his sperm. A year ago, his wife Kristin underwent in-vitro fertilization. The couple gave birth to their son, Luke, in October 1999.
Every six months, Armstrong is screened for cancer - his next screening is in October. Doctors say there is only a 1 percent chance the cancer will return.
Asked what his proudest achievement is, he answered quickly: "I prefer to be known as a cancer survivor. It's my proudest achievement."
If Armstrong wins the Tour de France next year and the year after - and very few doubt
his ability to do it - he will tie the all-time record for the international race.
Another achievement? His wife is expecting twins in December.