The referee in football doesn't rule the re-kick rather the team that reaps the benefit of a penalty and chooses to re-kick. For instance; if a punt only goes 20 yards on a 4th and 12 punt and the defense was offsides; the referee just calls the penalty; the kicking team selects to enforce the penalty or re-kick.
My answer - a referee seldom rules a punt to be rekicked. The kicking team will have that luxury ONLY if a penalty flag was thrown and in their favour.
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