Yeah, and also in general when you apply to become a national of a country (at least in the EU as far as I know, but every country has their own process), you have to present both your parents' birth certificates. They can then check if you're argentino de origen or not.
The term "de origen" doesn`t exist outside of Spain so its no possible to proove it for most of countries, as such term will be not written in no document- nobody fits?)
BTW Spain doesnt ask for parents` birth certificate, only certificate of the applicant him/herself.