Probably it's a matter of % of their total diet, not just eating an occasional leaf. the same with fish meal, or any strong tasting ingredient.
Also, is it actually true, or more 'old wives' tales'?
Mary
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Your easiest plan would be to use deep litter in the runs, because the total run space that you have per chicken really won't allow rotational grazing without overcrowding the two pens while the third regrows. Bagged shavings, wood chips (not all black walnut or cedar), grass...