Yeah, it all made sense in the end for Snape. Early on in the books/movies, it was pretty vague but given that Snape & Dumbledore knew each other since Snape was a student in Hogwarts, the trust is definitely established. Snape wasn't an evil person, he's not going around killing people for the sake of it. He was a Hogwarts teacher and to some extent, Dumbledore trusts his teachers.
