Free range hens eat as much vegetation as they want, without scouring. However, they choose for themselves what they eat, so if for example you are feeding lots of brassicas to your hens I can see that that might make them scour, as they wouldn't be choosing a balanced range of greenery. Another point is that for your ex-bat, used to dry food for all her previous sad life, suddenly having all the greens she can manage could cause her some digestive problems. Every now and then one of our hens will get a dirty bum so we dag it as we would a sheep - hens can get fly strike too. You could try cutting down her greens by half and see if that clears her up. If it does, gradually increase the amount and see how much she can take before she scours again.
The scouring could also be something else altogether - people who know more than I do should have suggestions.