'What you're saying is "I, a white person (the supposed "person of privilege"), realize that I am in a superior position than you, a mere (insert non-white person here), simply by virtue of the color of my skin. Therefore, I, a magnanimous white person, will do what I can to help you! Aren't you blessed!"'
No, not at all, that is a complete misunderstanding.
It's about being aware of the history and mindful of your own behavior.
It's naive to think that skin color doesn't still have a significant impact on the way people are treated.
You seem knowledgeable enough that I assume you have an idea how much more often someone is likely to be stopped/shot by Police if they don't have white skin.
How much more likely it is that someone will assume you are a criminal if you don't have white skin.
There is a disproportionate number of poc in the prison system.
It's not about being some superior white saviour, it's about acknowledging that historically, white people have been dicks and now without making a fuss about it, it's the decent thing to do to balance things out when the opportunity arises.