If the USA allows "Oh NOES! Teh cartels are after me" as an excuse for asylum, we'll soon be over-run by Mexicans...oh wait...we already ARE getting over-run by Mexicans...and we DO NOT need any more...
So no Mexican, legal or otherwise, should be granted permission to enter the U.S.?
I'm not sure I understand the concern about setting a precedent that would allow any Mexican to be granted asylum. Asylum is dealt with on a case-by case-basis. Refugees and their cases are thoroughly examined and reviewed before asylum is granted. Hordes of people wouldn't be able to come to the U.S. through asylum because it is difficult to attain. The same goes for any other legal way of applying for legal immigration, which is why so many people immigrate illegally.
If the southern U.S. is being overrun and damaged by anyone, its
illegal immigrants, not asylum seekers like this girl or any other
legal Mexican immigrants.