[masonic]

  I don't think that contradicts the other comment.

Sure it does; "were all here on legal visas" is false.

  That some of them overstayed or didn't meet the terms of their visas

Even those that did have legal paperwork all obtained it via fraudulent means by lying on their applications as to purpose of visit; technically speaking, none was here legally.

[mikeash]

The point was that ignoring people with visas would not be compatible with a goal of keeping terrorists out. I (and I think the other commenter) don't think it's a good idea or worthwhile, but it does fit the stated goal.