Why add in the sibling thing? I get that he could pretend to be the son so he can stay and receive treatment,…
I don't think the translations were very clear about this, but I think the idea is that if Ah Ro doesn't know that he's illegally in the city as a non-noble, she's not complicit in the crime. It wouldn't be a crime for Ah Ro and her father to be housing her long-lost half-noble brother, but Moo Myung is, as far as we know, not at all noble and thus not supposed to be in the city at all.
Does that make sense? gah