A good remark, but also a word of caution.

The Syrian situation is not directly comparable. With modern logistics, it is way, way easier to feed even big masses of displaced people. We can produce food efficiently and we can move it over long distances before it spoils. If you run away from active fighting, chances are that you actually survive, even though the refugee camps are miserable.

Neither was true in the Early Middle Ages and if an invader displaced tens of thousands of people from somewhere, they would just die of hunger. The capacity to take care of sudden crowds of refugees just wasn't there.