I think we just have to accept that on faith. I mean, they were really pushing it in the scene where Kara reveals her secret identity to Nia. She didn't even change into her Supergirl costume. She just took off her glasses and demonstrated that she could fly, and Nia is all "Ohmigod, you're Supergirl!" even as Kara is standing there in her civilian garb, just minus her glasses. And then there's Lena Luthor, who is a super-genius, but can't see past Kara's brilliant disguise.