Doesn't Kylo even tell Rey "You know it's true" when he reveals that her parents were nobodies? I think that was the entire point, to hammer the fact home, that she was hoping that she was more than just some junker kid abandoned by deadbeat parents, but was in denial about it. It absolutely felt to me as if it were meant to be definitive. It's like, the entire point of the movie and, seemingly, the trilogy. Not sure why so many fans are still latching onto the conspiracy theory level belief that they are just going to come out in Ep. 9 and be like "J/K Rey your dad is really Obi Wan!"
Yes, Kylo says that. As he's telling her that the Resistance is doomed to fail and that if she joins him they can create a new and better empire, etc... That entire section of dialogue from him is his gaslighting Rey to make her join his side.
Kylo Ren: Do you know the truth about your parents? Or have you always known? You've just hidden it away. Say it.
Rey: [in tears] They were nobody.
Kylo Ren: They were filthy junk traders. Sold you off for drinking money. They're dead in a pauper's grave in the Jakku desert. You come from nothing. You're nothing. But not to me.
Classic gaslighting. It's also telling that he says they're dead in a pauper's grave on Jakku when Rey saw in her own, non-Snoke-invoked vision that they left Jakku.
Well, he said it directly.
When Rey got a flash of his future while they were connected, he got a flash of her parents which is how he learned who they are.
Snoke manipulated everything that the both of them saw to orchestrate Rey coming to the ship. Kylo says he saw Rey's parents during the same vision that Rey has where she says she saw his future. The truth is, neither of them saw anything specific and they couldn't have as even Snoke couldn't see the specifics.