14U, knowledgeable coach (I thought). Coach is also commish, and responsible for paying me later.

2 outs, 0-2 count, foul tip, picture-perfect, one for the rulebook picture beside the definition of foul tip. Batter's out.

Conversation occurs civilly while teams are changing sides.

Coach - Hey blue, why is my batter out?
Me - Catcher caught it - foul tip.
Coach - That's only if the ball goes over her head.
Me - Uh, no. That would be a foul ball. This was a foul tip, it went right from the bat to the glove.
Coach - I'm sure you're wrong, but no big deal.
Me - If I'm wrong, you can keep my paycheck for the week. If I'm right you pay me twice for this game. Look it up when we're done.

After the game...

Coach - Looks like I don't have to pay you this week. Says right here' it's a foul tip when the ball goes straight from the bat to the catcher's glove.
Me - Yes. Thank you for proving my point. That'll be $XX please.
Coach - but it doesn't say anything about her being out for a foul tip. It just says it's a foul tip.
Me - We can escalate this bet if you want... but look under "The umpire should call a strike when..." first.

After the next game...

Coach - So it just says that foul tip was a strike, not an out. Why was my batter out?
Me - It was 0-2.
Coach - right, but the foul tip should have been a strike, not an out.
Me - Right - what happens on strike three?

And I see the light bulb go on.

One note - even though this was kind of funny, I'd work for half if every coach had A) the same demeanor as her when disagreeing with a call and B) the same desire to actually understand the rules instead of just knowing enough of the rules to give them things to complain about. This lady's actually great to work with/for.