Baseball Question: Solution

OK, as promised I am posting the solution to the Baseball "Heichi Timsa" from yesterday. Just to acknowledge, the solution posted by Air Time is valid in a "brute-force" kind of way, but is probably even less plausible than the "real" answer that Phil Rizzuto gave! Plus Rizzuto's answer - which again he claims once really happened - is more elegant in that it only requires two men on base, and - more significantly - the three outs are for three different reasons!

So, without further ado:

1. No outs, men on first and second, batter hits a pop-up to the 2nd baseman.
   
2. The infield fly rule is invoked and the batter is automatically out.
   
3. The runner on second correctly retreats to his base.
4. The runner on first, under the misconception that the batter had a hit, keeps running and passes the runner on second, therefore being called out.
5. The pop-up, instead of being caught by the 2nd baseman (which is superfluous since the batter is already out as per #2 above), lands on the runner on second - who is then called out for making contact with a batted ball.
6. Ergo, three outs are recorded and the inning is over - without any fielder touching the ball after it is pitched!