Poor reasoning. By that standard the Native Americans should shut up about all the wrongs white people did since they had participated in killing each other off long before the Europeans arrived. Unless you're one of those people who think Native American wars were more "pure" than white people wars (yes, I have actually heard that argument made before).
On that note, the article almost treats Mexico as if it is a country that's just always existed since the dawn of time. How does Robyn Pennacchia think Mexico was founded? Some Europeans came along, conquered a bunch of Native Americans, took their land to establish a colony, which eventually declared independence...is this sounding familiar to any other Americans? Obviously the details are different, but the overall history has a lot of similarities.
Just to be clear, I do think the United States' immigration policies need a drastic overhaul, and I do think there is much more whining than anything actually being done to fix the issue. Some of the things noted in the article are certainly true (the Mexican-American War is among the least justifiable conflicts the US ever got involved in). But it's an example of half-ass done history and inconsistent reasoning.
This brings me back to a point I think I've mentioned here before. There is almost no place on Earth that hasn't been acquired through violence and conquest. If we're going to say "such and such people were here first" it's going to take a very long time to wade back far enough through history to put everyone in the right place.