Ethan knew that getting closer to Nathan was the worst strategy ever to get to talk to Hazel,he needed to see her but the report he got from the men he sent to keep check on her was futile.
Nathan was a corky bastard back then in highschool so there's nothing that was going to work out between them but he had to try,meeting him at the hospital was a coincidence.
At First he thought of the reason why he was at the hospital,he thought it was Hazel that was sick but his friend got his mind calm down when he gave him the information about who he came to see.
Of all the people, why do you think Nathan would care about Hazel?
He knew how cunning and manipulative he was back then in highschool and it was no secret that him and his elder brother wasn't on good terms,so it's not a good idea if he went to the hospital to see Hazel when he would be the happiest if anything happens to his brother's fianceè.