Interpretation has nothing to do with it, you have a whole great grandfather because the 14th amendment says you do. It fixed an existing problem with the original document, and it did so with the approval of the state legislators (albeit with some coercement in the warmer climes). If some random federal judge had ruled your ancestor equal to 1 person, he would have been ridiculed as though he enabled the state to strip you of property for third party gain, or something else just as assinine.

Look at the proposal and ratification requirements for amending the Constitution (Article V), and consider the possible actors. The executive and judicial branches are completely cut out of the picture. Congress can propose amendments, but cannot ratify. Congress can be bypassed in the proposal step by the states with the national convention mechanism. The power to alter to Constitution lies with the people or the States, not the federal government which the document is meant to limit.