My reading of the article suggests that the form was for the right person, but was filled in ticking each question the opposite of the way it should have been filled in. My conclusion is that adding someone to the no-fly list is purely a box-ticking exercise (in the literal meaning of the phrase), without actually requiring any written reasoning or any proof of anything.
I've just realised that the idiom 'checking boxes' might be foreign to you. In this case, the 'boxes' are squares on a piece of paper, and 'checking' them refers to filling them with a tick-mark.
I managed to avoid using the term in my comment as I'm from the UK and it's definitely a US thing.
