It wasn't proven, but it was suggested that he was wrong. The story Kairi's grandmother tells presents a scenario in which the world began in light and darkness came later. Then there is Kingdom Heart, the place from which all things are born. Ansem SoD tried to use the true power of Kingdom Hearts, which he thought was darkness. However, it's true power turned out to be light which in the end ultimately contradicted his beliefs.
Actually, Kingdom Hearts is both Light and Darkness. It has equal amounts of both. So, it seems that Sora's Heart beleived in the Light more, than Xehanort's Heartless beleived in the Darkness. Thus when Xehanort's Heartless tried to use Kingdom Hearts power Light came out. The faith that Sora, Donald, Goofy, and even King Mickey and Riku in the Realm of Darkness had in the Light outnumbered and overpowered Xehanort's Heartless' faith in the Darkness.
Also, maybe both Xehanort's Heartless and Ansem the Wise are correct. In Kingdom Hearts: Re:Chain of Memories Reverse/ Rebirth, Riku awakens in Sleep and the last thing he remembers is being in the Realm of Darkness with King Mickey. So maybe things are born in the Darkness and awaken in Sleep.