It sounds like you're doing the right thing. She wouldn't have passed anyway, by the sounds of it.

This is exactly the sort of dilemma presented in Papers Please, which I can highly recommend. The banal moral conundrums are however punctured by nice moments of hilarity.

The developer also has a new game coming out. http://uk.ign.com/articles/2014/10/23/papers-please-dev-announces-return-of-the-obra-dinn