I don't think it would be exaggerated. Keep in mind armies enjoy bonuses to supply limits on top of that base value, when marching through "friendly" provinces. So the lords of Dorne could march armies of 10-12k through those provinces without hassle.
Dorne definitely needs to be a harsh place for invaders.
Oh, I thought he meant that only one thousand people can be at one province without attrition.
If it's 10-12k then it would surely work.