A few decades later, as Major League Baseball prepares to celebrate and honor Robinson's debut and his breaking of the color barrier 60 years ago, Reinsdorf recounts the tale with the passion most baseball memories bring about.
"It's a very sad story. I had one chance to meet him," said Reinsdorf with a smile during a recent interview discussing his connection to Robinson as a fan and beyond. "I was at Ebbets Field for a game and had general-admission seats. It was a packed house and I was there with a friend and someone asked if we wanted to be on the Jackie Robinson show.
"We were pretty sophisticated and said, 'You are just trying to con us out of our seats.' We refused to go. We didn't believe it would be Jackie Robinson, and didn't want to get out of our seats.
"Thirty minutes later, two kids came walking by and said they were on the show," Reinsdorf added. "I never met him. I never met him because I was too smart for my own good."
Reinsdorf had plenty of chances to watch Robinson, and was actually at Robinson's first game with the Dodgers. It took place a few days before his April 15, 1947 regular-season debut, as Robinson was brought up to take part in the traditional home-and-home series to end spring between the Dodgers and Yankees.
As an 11-year-old, die-hard Dodgers fan, Reinsdorf and his friends had only one question concerning Robinson. Could he play the game? Robinson quickly provided an on-field response to that particular inquiry.
"I was only 11, so I wasn't into the politics. It didn't seem to be a big deal among us kids," said Reinsdorf of Robinson, who played for the Dodgers from 1947-1956 and took part in six World Series. "He came up with Spider Jorgensen, and Jorgensen got off to a much better start than Robinson. I remember Robinson was only batting .240 into May, so there was some question about whether he could hit or not.
"He came on and hit .297 for the whole year. For the first couple of years, you didn't realize how fiery he was. That was kept under wraps. In 1949, when [Branch] Rickey said 'be yourself' and he hit .342 and became MVP, he also became a very outspoken guy."
Memories of Robinson, both as a person and as a player, race through Reinsdorf's mind. They are delivered with the precise detail of a man who was not only in charge for Chicago's only World Series title in the past nine decades but also an individual who loves the game. Reinsdorf spoke of Robinson causing more balks than any player he had ever watched, dancing back and forth on the basepaths and distracting the pitchers.
And then there was Robinson's ability to steal home, which he accomplished 19 times during his illustrious career. Reinsdorf also remembers a unique move belonging to Robinson, where he would hit a single to right and take a big turn around first base.
If the right fielder threw behind him, Robinson's great speed would have him on second. If the right fielder threw the ball into second, Robinson retreated back to first.
"Nobody ever caught on to it, and he always knew what the outfielder was going to do," Reinsdorf said. "He was probably the most exciting player I've ever seen. He had more ways to beat you than anyone else. He could hit for average and hit for power. He could steal a base. He could bunt. He was an incredibly competitive and intelligent guy.
"Jackie Robinson probably was the greatest athlete of the 20th century. He led the nation in rushing in football [for UCLA], with a 10.5-yard average. He was an All-American basketball player, a world class broad jumper and, of course, he played baseball and was a junior tennis champion. Who has better credentials than that?
"When ESPN named Michael Jordan the greatest athlete of the century, I thought that was ridiculous compared to Jackie Robinson," Reinsdorf added. "Michael was fabulous at one sport, but Jackie was dominant in all of these."
The White Sox chairman also expounded on Robinson's great intellect, a college-educated man who was one of the few black Republicans. He was a big supporter of liberal Republican Nelson Rockefeller, according to Reinsdorf.
"He had his views on all sorts of things, and he didn't hesitate to express them," said Reinsdorf of Robinson.
In praising Robinson as a player and a person, Reinsdorf never loses sight of his most historic contribution to the game. In fact, others among the White Sox staff, such as Ken Williams, the lone African-American general manager presently in baseball, appreciate Robinson's important contribution to society as a whole.
Before the start of Spring Training, Williams had the chance to attend a Muhammad Ali fundraiser in Scottsdale, Ariz., and also had the chance to talk with both the champ and basketball legend Kareem Abdul-Jabber, who was a guest in attendance. Williams thanked them both for the sacrifices they made to help later generations achieve and succeed.
"I'm keenly aware of the sacrifice and inroads others have made to help me sit here in this chair right now," Williams said. "That just takes it a step further when talking about Jackie and others from different walks of life, as well. It was an important time of life in our history, not just for African-Americans but for everyone. We needed to evolve as a people."
"Had [Robinson] failed, it probably would have been a number of years before blacks came into the game," Reinsdorf added. "Sooner or later, they would have come in. The world had to change. This nonsense had to go away at some point. But it was Jackie Robinson's immediate success that brought Larry Doby in a matter of a couple of months; he opened the floodgates for African-Americans to come into the game."
On Sunday, April 15, Jackie Robinson Day will be celebrated across baseball in honor of his legend. White Sox first base coach Harold Baines, third base coach Razor Shines and right fielder Jermaine Dye will all don jersey No. 42 in Robinson's memory for a scheduled game with Cleveland at Jacobs Field.
Today's younger generation of fans know of Robinson's historic role but might not appreciate his immense skill and success as a player. Reinsdorf has the unique ability to address Robinson's impact on all levels.
His only regret might be hanging on to Brooklyn Dodgers tickets many years ago and missing out on a chance to meet Robinson, although Reinsdorf did meet his wife and daughter in later years.
"I don't know what happened to the 60 years. I was 11 and now I'm 71 -- I'm more worried about that," said Reinsdorf with a laugh. "I'm not sure today's players appreciate the significance of Jackie. They should think about him every day. He broke a barrier that was not easy to break.
"People who are older than me are dead. People younger than I am, they didn't see the things I saw. I came into the tale end of the South, where you would go into a public facility and see colored and white water fountains.
"Joe Black once told me that all the players could stay in the same hotel in St. Louis, but the black players couldn't use the pool," Reinsdorf added. "I saw and heard things like that and I couldn't believe that's what went on in our country at one time.
"But I never heard of anyone in Brooklyn who didn't want Jackie Robinson in the game. I'm sure there were racists, but no, he was a fan favorite because he was exciting."
Scott Merkin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.