As shown in Birth by Sleep, Aqua accidentally gave Kairi the power to wield the keyblade. In KH2, Riku gives her a keyblade. 3D has Yen Sid talking about Kairi being a keyblade master. Since Kairi had her nobody created in KH1, that must mean that the power to wield a keyblade already happened. Sora gave that power to Roxas, so Kairi must have given that to Namine. Right?