Mail stops arrows well enough, at least at longer ranges. Although I'll readily admit I don't actually know what the main doctrine of the Armenian, Parthian, Sassanid etc. archers was...

Anyway, mail hauberks and large shields served the heavy infantry of the Crusader states well enough against Arab and Turkish archery, and for that matter that of said nations as well. So I sort of doubt that was the prime impetus behind the devlopement of the segmentata. Contact with cheir-type laminated limb defenses and the appreciation of the basic principle combined with developement of sufficiently mad ironworking skillz would sound more likely to me.