Then that assumption is outdated, which is fine as long as, now knowing that, it is appropriately adjusted.
You can sorta refer to white people in that way but it doesn’t really have the same effect because of things like power dynamics and the fact that we are able to know where we’re from quite easily. For Black people it’s a cultural identity they needed to build nearly from the ground up, for white people it really is just a way to talk about a group of people based on their skin colour and generalized stereotypes. No one is White because they have connections to their more specific history, but many people are Black precisely because they don’t.