I think it's a question of degree and this could only be answered by playing the original mouthpiece and the D'Addario back to back.
Taking your statement to extremes, given the acknowledged inconsistencies in Links and modern Meyers this is like saying there is no such think as a link or a meyer because the smallest of changes can have profound effects. Also any refacing of a piece no matter how minor or simply corrective renders it a different piece - no longer should it be called a link or <insert other mouthpiece>. You could even argue that there is no such thing as <insert mouthpiece type> because the facing is different depending on which tip opening you choose.
However we know in practice that links have common characteristics that are not lost when they're refaced, and that within a line of mouthpieces changing tip opening still retains the basic feel / flavor of the piece.
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