'I haven't an opinion' is totally normal in British English. I was even taught the avoid the unnecessary word 'got'. Why do I get marked down every time I avoid 'do' and 'got'? You don't hear it in these islands-unless you are speaking badly or it's dialect. My greatest language problem with duolingo is this battle with 'American'!
I'd say that when we in Poland learn English, we learn "do not have" as the most obvious way to say this, and "have not got" as an alternative. It wasn't until I started moderating this course that I learned that "have not" on its own is correct. It's still hard for me to get used to it.
The people who created this course also clearly didn't know that. So right now I am adding it wherever someone asks. But perhaps it's safer for you to start using "do not have", it would be easier on your nerves ;) Or you can be the person who fights for the acceptance of "have not" everywhere where it's needed.