MLB Rule: Was It a Fielders Choice? Analyzing a Close Play

Question
High School Varsity, 1 out, runners on 2b and 3b.  Left Handed Batter slaps it short to shortstop who fields it clean, looks to first, runner is already too close, looks to home to get 3b out but they are also too close, 2b runner hesitates then heads to 3rd.  Shortstop tosses to 3rd and gets the out.  Batter was given a FC even though they would not have been thrown out, and the 2b runner didn't have to go but did.  I think its a hit.

Answer
You are absolutely correct, it is a hit.  Poor base running by the girl on second doesn't make it a fielder's choice.

The most important requirement of a fielder's choice is that a normally played ball and a throw to first would have put the batter out.