The US citizen could be trying to work through the bureaucracy for a legal permit for, e.g., a father, cousin, wife, worker, etc. Not saying that it is necessarily the case in the story, but certainly possible and lawful. Similarly for “asylum” cases. We do have laws that allow entry for those who would be persecuted, under stated conditions in laws passed by congress. Many are phony, but many are not. Again, legit for lawyers to work on.
So I'm not surprised that these students are spending time on asylum cases, etc. (Despite the reporter's attempt to paint this as simply a "Mexican" issue, with that comment about why the clinic was created).