I've heard that one before and it seems to be one of the lesser-known "rule myths" that pop up from time-to-time.
The first time this came up a few years ago, I looked for any rule that would require a pitcher to leave her rosin bag on the field for the other team to use. I never did find a rule, Point-of-Emphasis, Case Book play or interpretation that supports this.
ASA rules do note that when a pitcher is using a rosin bag, it must be kept on the ground back behind the pitching plate. But that only means when that pitcher is out there pitching! She can take it with her between innings. Maybe some umpires read this and think it means left on the ground "all the time".
NCAA rules make it clear that it is the responsibility of the pitcher using rosin to remove it from the field between each half-inning!
Maybe some other organization requires the bag to be left on the field all the time, but until somebody points me to that rule book I'm going to say that any umpire calling this is making stuff up!