I think they're saying that case d specifically is not a legitimate proof, or equivalently that instances of case that are legitimate proof can be made construc

I think they're saying that case d specifically is not a legitimate proof, or equivalently that instances of case that are legitimate proof can be made constructive through a trivial addition (eg https://news.ycombinator.com/item?id=20395476 https://news.ycombinator.com/item?id=20395476). I suspect they are mistaken, depending on how one defines "demonstrate" and "specific", but you haven't actually shown that.