I'm 30, it's been that way for a LONG time, maybe always was, dunno.
I don't know of any "incident" that caused this policy.
Before 1920, the baseballs were considered property of the team and fans were expected to throw them back if they were hit into the stands. Sweeping changes were made to the game in 1920 to make the game more fan friendly and to add offense to the game. One of those changes was allowing balls hit into the stands to be kept by the fans.
Actually the policy changed with the Giants in 1921, and was gradually adopted by other teams over the next few years. Before then, fans had to throw any foul ball back to the field (a practice that was still common in Japan until the late 1990's).
On May 16, 1921, Reuben Berman refused to throw a ball back at a New York Giants game at the Polo Grounds. He was escorted out of the stadium, and later sued the Giants for mental and physical distress and won the court case plus $100. The Giants changed their policy. (Source: The Dickson Baseball Dictionary, 3rd Edition, 2009, p. 703 "Reuben's Rule.")
In Pittsburgh a few months later, 3 fans were arrested for keeping foul balls. The city basically instructed their policemen to stop arresting people for this, and the Pirates changed their policy.
Prior to this, the Cubs allowed fans to keep foul balls as early as 1916. (Once the Phillies played in Chicago and requested compensation for 8 lost balls during batting practice.) An 11-year old boy in 1922 was arrested for this crime in 1922, spent a night in jail, and was exonerated by the judge who dismissed the charges. The judge commented "Such an act on the part of a boy is merely proof that he is following his most natural impulses. It is a thing I would do myself."
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