Well, the author of the article is assumedly from the UK. In general, this is not what they would say. They would say something like "respectfully, I'm not sure that's correct". One is a lot more "direct" than the other.
More like "Are you sure? I'm worried that <opposite of thing interlocutor just said>." or "Sorry, I think it's actually <opposite>". Both in an apologetic tone. The word "respectfully" sounds like it's trying too hard: it's a bit overtly subordinate and ingratiating.