Batted ball goes foul ?

Question
On my grand daughters team, a girl batted the ball toward the pitcher and the ball hit fair but rolled back to the plate. The catcher picked the ball up and stood with the ball while the opposing team player ran to first and stayed on first.

The opposing team coach and umpire called the ball fair. The play continued with the next batter.

Were they right or wrong ?

Answer
Hi Carl,

Thank you for your question.  I wish I knew EXACTLY where the catcher picked up the batted ball.  It was a FAIR ball if the ball was:
1) on or over (above) home plate
2) from the catcher's point of view, in front of home plate
3) on or over (above) one of the actual or imaginary foul lines that extend from 1B and 3B to the rear point of home plate
4) from the catcher's point of view, on or over (above) to the right of the third base foul line, or to the left of the first base foul line

Otherwise, it was a FOUL ball.

Scott Kelly