Maybe he didn't see it hit the fence?
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As long as it doesn't touch the fence, yes. Once a ball touches the fence it is live and it may as well have touched the ground.
He must be thinking of a ball that touches a fence in fair territory. The one in the OP touched the fence in foul ground, so it became a foul (dead) ball.
Not an out unless there were two strikes already and that made three.
This is not a valid catch for an out. Once the ball hits anything other than a defensive player it is no longer considered to be airbourne or in-flight. This should have been just a plain old foul ball.
One of our team mates hits a foul fly.1st baseman catches the ball , it bounces out of his gloves hits the fence than caught it again.Our batter was called out. Was this the right call?
If he actually caught the ball, as your post said, then it was the right call. If the umpire thought he was transferring the ball to his throwing hand, and it hit the fence in the process, then it sounds like he made the right call. If the ball just hit off his glove, then the fence, then back into the glove, then no, it's not a legal catch, and not a good call.