[Citation needed]
I don't think you could find an example of even one feminist claiming that you can't find representation from people with different demographics to you. This is not what people are claiming when they say "representation matters". In fact, minorities are MUCH more likely to find representation outside their demographic, out of necessity if for no other reason. What people are claiming (many from personal experience) is that a lack of representation in a given pursuit makes it harder for people to imagine those pursuits as something available to them.
In other words: Yes, a black woman can empathize and relate to characters of any gender and race. But that's not a good argument that we shouldn't correct the underrepresentation of black women in media and STEM. It's also not an argument that black women won't be helped by seeing increased representation in media and STEM.
I'm assuming this is a good faith misunderstanding, but if it's not, it's a very good example of what you call "twist and manipulate words to fit any meaning they want to ascribe".