I'm afraid it's the old "search your feelings, you know it to be true" thing. Deep down Rey always knew she was abandoned and she eventually she admits it. Her parents were nobodies who simply didn't care about her.
Thankfully you don't need to be from a special family to be a hero. That's the whole message of the movie. Rey, Finn, Holdo, Rose, etc are just people willing to fight for the cause. They don't need to be part of the Skywalker family to do that. The movie ends by implying that there are other nobodies out there who could become heroes too.