Let me try this as Pool Hustler has set the stage here, and Bob has said his approval on the first two outs ...
Infield fly rule must be involved somehow. I can come up with a double play adding the trailing runner passing the lead runner while the ball is in flight. But the third out? You got me on that one.
Because the infield fly rule is called, yes the batter is automatically out for the first out. And yes, what pool hustler said with trail runner (runner on 1B) passing the lead runner (runner on 2B) for out number two. When the infield fly rule is engaged, the other runners on base can advance on their own accord. Thus, our lead runner goes back to second base and tries to tag up and advance to third base but he is somehow called out on interference with the fielder covering second base while in the midst of trying to tag up.... A triple play
without the ball being fielded.
However, if it is fielder obstruction based on the umpire's decision, then the umpire would award our lead runner third base. Therefore, it would only be a double play and
not a triple play.
Either way, it would look like mass confusion on the basepaths... be it a double play or a triple play.