"I have got a friend" Is this Grammatically correct?

I have a concern. It stems From Lesson “6. I Have a friend” by evgueny40 from “Let’s Start!” series in English. The line reads. “I HAVE A FRIEND I have a friend. = I have got a friend.”
This sounds wrong to me. I don’t believe you should have “got” and “have” in the same sentence. Yes “I’ve” means “I have” and you could say “I’ve got”. But I believe it should either be “I have”, or “I got” but not both.
Also. Why is it that I can’t ask a tutor directly from the lesson?
No… this isn’t for my benefit I am a native speaker of English. I have a friend who is learning English here at LingQ and she brought it to my attention. By asking me a question to which of course I told her “no, you can’t say that, it isn’t grammatically correct”. Then she showed me this lesson.
Please help. Am I confused? or is it Wrong?