As you point out the media does not want the commentators to use precise language when speaking on this issue. Illegals are called “immigrants” in the media storm — it confuses the issue and thereby puts the decision making in the hands of “those that care the most” — the leftists.
They say Mexican-Americans which is a special term they have taught those of that heritage to count themselves party to, even as citizens of the third generation, and then they use it for Central American illegals that the Mexican government is dumping at our borders illegally.
No clear path to better government and good reform from catastrophic conditions can be found when debate and discussion cannot be done with precise language. The media is getting the chaos they want.