I am not sure if this will make you feel any better. I am a native English speaker with an English/Irish/Canadian name who attended an English language high school, but in the province of Quebec. This was before the TOEFL existed, but a well know American university did require that I go into downtown Montreal and chat (in English) with an alumni to show that I could speak English well enough to attend university in the US. It is a good thing that the chat was in English, because it is the only language that I could ever speak well enough to attend university in that language (I could have chatted pleasantly in French, but I could not have attended a French language university).
The world is full of silly requirements. Taking the TOEFL seems low on the list of silly things that someone is going to ask of you.
Is your bachelor’s degree from a university that teaches in English? By the time that I was applying to graduate school, having a degree from a US university did seem to be sufficient proof of my proficiency in English.
How will CMU know that English is not your native language or one of your native languages? I have known people who had two different native languages, both of which they had learned to speak starting approximately at birth.