You are correct.
In English, the response mirrors the grammar of the original statement. If someone makes a negative statement, you agree with it with a negative statement. These grammatically negative responses are often accompanied by a 'No'. For example:
"That's not right, is it?"
Agreement: "No, it isn't" (certain)
"No, I don't think so" / "No, I don't think it is" (more tentative)
Disagreement: "Yes, it is" or "Yes, I think it is".
I realise that it seems strange to learners that we sometimes agree with a 'No' and disagree with a 'Yes', but that is what we do in English. The negativity refers to the grammar of the statement, not the view about whether or not the original statement is correct.