You bet they do. Living in the southwest all my life, I have many friends and associates of Mexican/Hispanic decent, that are truly damn good Americans.
And you are so correct, they will be the first to point out that we are a bunch of suckers. And any illegal, if truthful, will completely agree.
When it comes to immigration, the last 30 years of this continued "free for all" is a national disgrace, and now a total national security nightmare.
Many of my friends in the southwest thought 9-11 would have been enough to wake up our leaders.
We were wrong.