To be fair to her, why would it invalidate her argument?
If you benefited from something you can't say it's bad? What kind of logic is that.
If one of your parents or ancestors had a baby from a rape, does that mean you have to be okay with rape or else you're a hypocrite because you wouldn't exist without it?
If your dad was corrupt and made millions stealing life-saving drugs from hospitals and selling them on the black market, then you have to support illegal drug trade?
If you oppose low-skilled immigration then I don't see where your parents or ancestors come into the logic.
I'd understand if she said this while actively trying to imigrate but this just seems like "Richard Dawkins ancestors owned slaves!" nonsense.