If someone who doesn't know your background says that you sound like a native speaker, it means they probably noticed something about your speaking that made them realize you weren't a native speaker. In other words, you don't really sound like a native speaker.
生い立ちを知らない人にネイティブみたいに聞こえるよって言われたら、それはおそらく、あなたの喋り方のどこかが、ネイティブじゃないと感じさせたってことだよ。つまりね、ネイティブのようには聞こえないということなんだよ。