Well yes feudal societies do have laws, many of them very good laws too.
But what matters is the administration of the system not just the written law itself.
What matters as well is the health of those who seek the protection of good laws,
it may suddenly undergo drastic decline.
However good the law, in a feudal society the outcome is decided by rank, connections, cronyism, and money.
The people who are fleeing may have genuine need, but too often they bring with the mind-set of a system based on submission, the acceptance of crime as the only way to make economic progress, and the legitimacy of violence. If there are a few, they can be accommodated, trained, educated and assimilated.
A Filipina is our country explained why the family fled from the Marcos regime. The family ran a fishing business, they owned a couple of boats, boats were routinely stolen, they knew who by. 'Why not go to the police?' They charge too much.

I would not be surprised but that is not the issue.
Prayer rugs and diseased children are smoke screens.
The entire question of mass immigration from feudal nations to nations with long traditions of rule of law, and all the other things we on here write about, is the concern. It is not just the lure of high wages, social security, free education and health care. .

It certainly doesn't ring true. It certainly seems like we can handle infectious diseases if we put our minds to it.