Sure they do. There's nothing illegal about rendering aid to the victim of a crime. Further, there's nothing illegal about paying for his hospital stay if you desire to do so.
So Jesus used the equivalent of a despised illegal alien..
Here's where you're on shaky ground. Where exactly in Luke does it say the Samaritan was where he was illegally? Chapter and Verse if you please.
L
Reread what I wrote with emphasis on "equivalent".