First, in the situation in the little league game tonight, that would not have been the case. And second, I believe Fielder still would have gotten the batter out even if he was running.
But that is beside the point ... the defense was given an unfair advantage (A catch would have resulted in one out but the drop resulted in two outs). In my opinion, The runner should be allowed to remain on the base until the batter arrives because it wouldn’t give the defense an advantage but also doesn’t penalize the offense.