Not to be picky sarge, but dictionary.com defines immigrant as:
im·mi·grant ( P ) Pronunciation Key (m-grnt)
n.
A person who leaves one country to settle permanently in another.
A plant or animal that establishes itself in an area where it previously did not exist.

adj.
Of or relating to immigrants or the act of immigrating.
Therefore anyone who chooses to settle in America is an immigrant, whether they do it legally or not, making the term valid.


Other than that I agree with you completely.