He's absolutely correct. Hispanic is an ethnic designation which has to do with culture and is self-identified. It is a binary system, you either identify as Hispanic or you don't.

Racially, Hispanic people are typically a mix of African, Native American, and European populations in varying proportions. You also have populations that are almost entirely Native in ancestry and culture, populations that are almost entirely African in ancestry and culture, and populations that are almost entirely European in ancestry and culture. All of these groups are under the massive umbrella of Hispanic.

It's like trying to judge my American-ness. I'm white, speak English at home, and enjoy hamburgers. There are plenty of non-Americans this applies to, there are plenty of Americans it doesn't apply to. You're either a US citizen or you aren't, nothing else matters.