It seems like the authors of the article are having a hard time reconciling the item as Spanish since it doesn't look Spanish. Military, Explorers, Conquistadors, etc. weren't all pure Spaniards. Carlos the 1st was the Spanish King during the big wave of Conquistadors (when Mexico, Peru, Guatemala, the Caribbean, and Florida came under Spanish control), he was also Charles the V over the Holy Roman Empire that controlled Germany, Austria, Hungary, etc. His son Phillip the 2nd was King of Spain, part of Italy, the Netherlands and England for a while. The Conquistador of Venezuela and Colombian was German, many of the soldiers who conquered Argentina and Chile were Irish. Several of Cortes' bigger group in Mexico were French, Dutch or Hungarian.
As long as soldiers were Catholic and from the Hapsburg family area, I doubt they checked passports on willing bodies who carried their own gear. I could see a foot soldier carrying pieces of armor that his father or grandfather had brought back from another campaign. Or something he bought along the way for better protection.