Ah, I see - if one was incidentally born in Argentina, during a vacation or something? Then I agree.
Though one could be born to non-Argentine, non-Hispanic parents permanently living in Argentina, be raised there and identify as Argentine primarily, and I would consider them Hispanic.
ETA:
This is a difficult term to apply in this situation. What constitutes being a native Argentine? Descended from the indigenous peoples that lived there prior to European colonization? Being a second or third generation Argentine? How does one define being a native Argentinian when 80% of its citizens are of European descent? Quite easily, the Italian or Taiwanese person could be a “native Argentine”. And with Argentina’s overwhelming Italian population, it wouldn’t be surprising.