I listen to NPR all day. Today I heard this story today (most of it) and have come to a conclusion that I think is sound and settles the argument and provides a win/win situation for just about everybody.
Because we live in the United States of America, where people are presumed innocent until proven guilty in a court of law, they should be referred to as "undocumented" until a verdict is reached. If they are found guilty in a court of law then they are referred to as "illegal."
