You are factually correct but in all honesty, and I mean no offense, I think it's kind of silly to worry about stats in 12U rec. My son was a pitcher in 12U rec and believe me I understand, but if I wanted accurate stats I made sure to keep them myself.
Gosh, no matter the age in rec., all that is kept is the batting order and runs scored, around here.
IME, you are lucky enough in rec league to find someone that wants to score, forget an experienced scorekeeper. A few years ago all the teams in our division were on Gamechanger. At the end of the season I reviewed the other teams season stats and 3 of the 6 teams had not recorded one single Reached on Error (ROE) for their hitters team. I knew this to be untrue because my team averaged about 5 errors per game!
I wouldn't be too concerned about it unless you really want meaningful stats, if so, you need to train the scorekeeper how to correctly score the book.
p.s. I see your DD is a pitcher, did she happen to be the starting pitcher that game?
The HC asked me to keep track since he may be the all stars coach. He's a great coach and a numbers guy. For rec ball, I would like to just bat 'em and score 'em cause, it's just rec ball. where the girls should learn and have fun without any pressure.
keep track of runs and batting order, the rest does not matter