How is it that people over there can't see the difference between a chat-show host and a journalist?

An anecdote by way of illustration.

The late Sir Terry Wogan, on his early evening chat-show, had interviewed Sir Robin Day, a political journalist whose uncompromising style of interviewing had earned him the nickname of 'Grand Inquisitor'. Having completed that segment, Sir Terry introduced his next guest, Jane Fonda. As was customary on the show, Sir Robin remained on stage, to join in the general discussion segment later. During his interview with Ms Fonda, Sir Terry mentioned the then-current rumour that she had had a 'nose job'. Ms Fonda replied that it was nobody's business but hers. Sir Terry accepted this, but before he could move on, Sir Robin jumped in with words to the following effect:

"On the contrary, Miss Fonda! You are an actress and thus a public figure, whose work depends in large part on your appearance. Therefore anything which might alter that is a matter of legitimate public interest!"

Not saying who was right, of course. Just pointing out that that was why Sir Terry was a chat-show host and Sir Robin was a political interviewer. To Sir Terry, the matter was something his guest didn't want to talk about, so change the subject. To Sir Robin, an interviewee had avoided answering a legitimate question and must be held to account for it.

Some US chat-show hiosts seem to want to blur the line, which is not good practice.

Just BTW, the legal surname of the Royal Family is Mountbatten , not Windsor. Oprah interviewed Harry Mountbatten and Meghan (PFWOBWISHP) Markle Mountbatten.