Without that letter, would they be unaware of the immigrant's actual status ? Do you think they can place an N 400 applicant as a K1 visa holder ?Do you think that the copy of the expired GC/with the extension letter is not sufficient?
There is no trap. It is circumstantial. Each case is different. Each case has its own story. There are couple who don't share the same house, couples that spend time apart for various reasons and still get their citizenship under the 3 year rule.