It will sound more natural when "that" is added after believe.
Does it? I think omitting the "that" sounds perfectly fine.
That usage is somewhat dated according to writing style guides. It works but it's verbose without benefit.
음 실제로는 믿는다고는 얘기하지 않지 않나요
보통 -라고 생각한다거나 -라고 본다고 말할 텐데