Ah I see! Thanks for the explainer, I see where I misunderstood it.
I thought invidious got the entire video stream and streamed it back to the viewer - not just the link to it. So even if YouTube sees the invidious instance ip as the one grabbing the link, it would still see your ip as the one actually watching the stream.
I guess the bot related error I mentioned comes from when the server tries to get the stream link.
What a terrible day to have eyes