“According to US law right now, anyone in the world who manages to set foot here has the right to claim asylum.”
They can “claim” anything, and if it is for asylum, it has to be proved, I mean originally, according to the law.
Setting foot here mostly involves walking across the border, and, since all the Mexicans tear up thinking about Old Mexico, down to the third and fourth generation after arriving, they can’t claim asylum.
Anyone can claim asylum.
It doesn’t mean anyone is going to get it.