Well, I can't speak for parent, but those of us that aren't U.S. citizens are already having a hellish time.
To those of us with work visas, this is like saying, "if you're homeless, just go to your vacation home," and then being surprised that people without vacation homes express feelings of despair.
I think most people realize that people on visas can be in an additionally tough situation during layoffs.
I think the commenter's helpful suggestion has an implied "Unfortunately, this doesn't help everyone, but..." In an attempt to help the people it can help.
For people currently in certain especially difficult or unfair situations, it might hurt less to know that people are sympathetic, though they might feel powerless to help right now.
Knowing that, maybe some of the people getting the short end of the stick would prefer not to have that constantly articulated. I can only guess at when is the right time to articulate, and when to leave it implied.
To those of us with work visas, this is like saying, "if you're homeless, just go to your vacation home," and then being surprised that people without vacation homes express feelings of despair.