Depends. The borders were different back then. There are people in my family who are ethnically Polish but from White Russia, which is now known as Belarus.
Careful. The literal meaning would be "White Ruthenia" (Ruthenia != Russia). In general this etymology is complex, and politically charged[1], but deriving it from "Russia" is most certainly wrong.
But I agree with your main point - ethnicity and nationality gets more confusing the further back past we go.
But it's pretty obviously politically charged, as in "White Russia" strongly suggests a Russian heritage and maybe even implies they're rightfully a part of Russia. This narrative is very beneficial for some, of course.
On the other hand, "Ruthenia" is a historical region, with no clear connection to any existing country. Thus "White Ruthenia" sounds much more like an independent country. English doesn't make it clear, but in many slavic languages it's just "Rus". Historically there was also, for example, Black Ruthenia[1]. Similar controversies were related to Macedonia for example, and Greeks objecting to that name.
