Actually, I believe that Argentina operates as the US does with jus soli citizenship, so being born there to foreign parents would result in an Argentine citizenship as well.
And yes, under the US census definition, one with only incidental citizenship from Argentina could consider oneself Hispanic.
However, it’s not as if the US census is the only or ruling definition of Hispanic… but that’s where I’ll leave that discussion because while I disagree to an extent I easily see it devolving into an off-topic debate.