Naturalization is reserved for aliens lawfully present in the country. The freedmen born here were not aliens and were therefore ineligible for the naturalization process.
Well according to the opinion of several of the congressmen debating the 14th amendment, the process of converting the freedmen into citizen was regarded as "naturalization."
But understanding it this way only works if you read and accept that the debates on the 14th are critical to understanding intent.
The freedmen were "denizens." This status existed in English common law. They were forbidden to own land, had special taxes assessed on them, and were barred from certain vocations.
I have read many English statutes that dealt with this particular class of non-subjects.