I have British friends whose families originally came from India, Pakistan, Egypt, Yemen and Palestine. Their English is of course as "native" as mine. Silly notion to think it is not.

And I know what you mean about the language centers here. My wife interviewed in a few when she was looking for something to do and found them dreadful. She chose to tutor on her own and referred all her students to the BC when we left Doha the first time.