You've got to be feeling pretty stupid to actually get CAUGHT crossing the border from Mexico, when millions of ignorant mexican laborers managed to succeed in the attempt.
The guy was dumb enough to cross at a Port of Entry instead of hiking across the desert.
If you attempt to cross at a Port of Entry with bad documents or if you have other issues you are very likely to get caught.
If you hike across the desert, the odds are very good that you won't.