Interplay of Natural Parent and Paternity Statute

I am beginning work on a complex legal issue involving the interplay of the natural parent presumption and the disestablishment of paternity statute.  The natural parent presumption is found in Mississippi Code Section 93-13-1 (Rev. 2004) which provides that:  “The father and the mother are the joint natural guardians of their minor children and are equally charged with their care, nurture, welfare and education … If either father or mother die or be incapable of acting, the guardianship devolves upon the surviving parent.” The presumption is rebuttable, upon a clear showing that: the parent has abandoned the child; the conduct of the parent is so immoral as to be detrimental to the child; or the parent is unfit mentally or otherwise to have custody.  This has to be measured against Mississippi Code Annotated 93-9-10 which provides only limited situations where paternity may be disestablished.  The question is whether a legal parent who never disestablished paternity is on equal footing with a natural parent?  If paternity cannot be disestablished, does that not make the legal parent the natural parent by law?  Every case dealing with this issue was prior to the passage of 93-9-10 which is relatively new.