[argodad]

Originally Posted by fiasco

It's my understanding that when infield fly is invoked, the batter is out and the runners are free to advance at their own peril.

True.

Two situations I observed during my last two games.

First game, R1 on 2nd, R2 on 3rd, batter hits pop fly to F4, infield fly is called. F4 catches the ball as R1 is about 6 or 7 feet off the base when the IF is called. F4 throws the ball to F6 who steps on the base before R1 can get back. R1 is called out.

So, even though IF is invoked, the tag up rule still applies? (I apologize if I'm not using correct terminology here....I'm new) I thought, based on the rule, the runner had the right to advance, thus it wouldn't be a force out, but R1 would need to be tagged.

Correct call. Runners are not forced, but still are liable to be put out on appeal if they left the base before the caught ball was first touched. In this case, the throw to F6 was a live ball appeal.

Second game, same runners, same pop fly. Except this time, F4 drops the ball. I call BR out, then R1 breaks for 3rd base. She gets caught in a rundown and gets tagged out by F4. I call her out. My observer comes onto the field and declares that she should be safe, as the ball was dead on the infield fly.

He told me after the game that if the ball is dropped, the play is immediately dead and runners go back to their bases. I can't remember reading this in the rule book.
Help?

Your observer is WRONG. Your call was correct. He may have been confused with an intentionally dropped ball situation. In that case, the ball is dead and the BR is out.