Your own sentence makes my point. That they HAD removable "privileges" indicates they are different from "natural citizens" because a "natural citizen's" privileges are not removable.
No, the privileges were not removable - which is why such attempts were voted down in Congress. Misguided congressmen are forever coming up with unconstitutional legislation - fortunately much of it dies a quick death.
Were the "jus soli" theory correct, it would have prevented any attempt to pass such a law. The fact that they attempted to pass such a law demonstrates that the jus soli theory cannot be correct.
Let me reiterate. If the common understanding of the time was that being born here was all that was required, the idea of denying citizenship to those born here would never have been discussed. The fact that it WAS discussed, PROVES that "jus soli" was NOT the common understanding of the time. If birth on the soil was believed to imbue the natural right of citizenship, it would have been pointed out immediately by all and sundry that you cannot take away a natural right. It would never have made it as far as the committee, let alone be discussed by the committee.