Correct. While the Spanish were indeed very brutal, the reason the native peoples of the Caribbean were essentially wiped out was due to disease, not slaughter. It's the contact, not the behavior, that drove them to extinction.
The Spaniards, were probably extremely dismayed to see the Taino and other natives dying off, not because of their humanity, but because their labor force was destroyed. That led to the pan-Atlantic slave trade, and is why most of the West Indies are black today.
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