@XieShu
There isn't a perfect answer, just a long discussion to be quite honest. The student may have been logically sounding on what he wrote about. This is the TLDR, to be honest, and what I'm writing after is some half-informed philosophy info.
The question that the story gives resembles well to the thought experiment by Immanuel Kant (google "Kant's Axe"). Though there are some differences, especially in the consequences and motivations because for this situation you're risking yourself to be a kidnapper apparently.
For Kant's answer to his original situation though, he bases that you should tell the truth to the abusive husband that the wife is hiding in the house. This is due to his thing called the "Categorical Imperative," which also is a long drawn concept. Though for this, the categorical imperative stands that basically if what you're doing is contradictory if everyone else did it, then you shouldn't be doing it. So if you're lying to the man, then that means everyone else should lie too, which arrives in a contradiction in the universe if everyone were to lie. You cannot therefore lie, and so you must tell the truth to the husband.
There was/is a lot of discussion about this, and one of the more popular responses was whether it was okay to lie to specifically Nazis; hence why there was a reference in the manga. There can be more to say, but again it is a long drawn discussion.