I believe this did happen, pretty much exactly as described below. I hear about it while listening to a Giants game probably in the '70s. I think it was in Yakama WA in the minors. I was searching for that when I came across this.
Here's how it would have to happen, and it would have to happen EXACTLY this way, because of a few stipulations in the rule book. There'd have to be runners on at least first and second so that the infield fly rule would be in effect.
There'd be a towering pop-fly hit in the infield, somewhere near second base. Once the fielder settled under the ball, and the umpire judged that the ball could be caught with ordinary effort, that'd be your first out right there, and the ball hasn't even fallen to the ground yet.
Secondly, while the ball was in the air, we're assuming that the runner from first base was running on contact, while the runner on second stayed close to the base. As soon as the runner from first base passed the runner on second base, then the runner from first base is automatically out for passing the runner on second. That's two outs, and the ball still hasn't hit the ground yet.
Thirdly, the outfielder, for some reason, would have had to misjudge the ball, or else just completely step away from it, allowing the ball to fall untouched to the ground. If the runner on second base was standing just a little bit off the base, and that ball took a bounce when it hit the ground and bounced up and hit the runner on second, that would make him the third out. There's your three outs, with no member of the defense touching the ball.
A couple of notes on this...the runner on second base being hit with the ball would HAVE to be the last out. The ball is dead as soon as a runner is called out for being hit with a batted ball. Therefore, the theory that you can have a triple play with no defenseman touching the ball by having a hit ball bounce off of three different runners is impossible. Even if that did happen, only the first to be hit would be called out, and the play would be dead. Also, the runner on second base would HAVE to be standing just off the base when he was hit. Note under NORMAL circumstances that if a batted ball strikes a runner, whether or not he's standing on a base, he'd be out...as the base is not a sanctuary in this case. However, on an infield fly, even though the runner is still out if a batted ball contacts him when he is off the base...he is NOT out if the ball contacts him while he is on the base. The infield fly rule is the ONLY time a batter is protected from being called out when hit by a batted ball if he is on base. Now you all are just a little smarter, thanks to one of the best umpires ever to call balls and strikes on the diamond...and that'd be me!
Unassisted triple play
The unassisted triple play.
Runners on first and second. Batter pops it up and is out due to the infield fly rule. The runner on first passes the runner on second and is out. The remaining runner is hit by the pop fly. Unassisted triple play.
An unassisted triple play.
There have been 15 unassisted triple plays in the history of major league baseball, none of them by Yankees players.
According to the Society for American Baseball Research, there have been 13 unassisted triple plays in MLB since 1876, the first being in 1909. That would make the odds of an unassisted triple play about 1 in every 10 years. Interestingly, these things seem to come in groups. Six of the thirteen came in the 1920s. Three of the thirteen have come in the 2000s. And on top of that, there were unassisted triple plays on successive days in 1927. On May 30, 1927 shortstop Jimmy Cooney of the Chicago Cubs turned an unassisted triple play against the Pittsburgh Pirates. The very next day first baseman Johnny Neun of the Detroit Tigers turned an unassisted triple play against the Cleveland Indians. Click on the 'Unassisted Triple Plays in MLB' link below to see the list of players that have made an unassisted triple play. UPDATE: There was a 14th unassisted triple play on May 12, 2008 when Asdrubal Cabrera of the Cleveland Indians notched one against the Toronto Blue Jays.
Eric Bruntlett of the Philadelphia Phillies.
it's never been done.
There have been 15.