Look, let's say you go to your GP for an appointment.
It could be called a
Private Consultation in that no other patient is present in the room when you see the Doctor though
Private here in the UK could also imply that the GP was seeing you outside of the NHS and would bill you privately for his diagnosis of you.
It could probably also be called or at least implied as a
Confidential Consultation in that what is discussed remains only between yourself and your Doctor ... and obviously the Health Service via your records...
And according to your rules, you claim that since
Private and
Secret are synonyms, they are completely interchangeable so it could also be called a
Secret Consultation.
Now it's true that what is discussed during the consultation would perhaps remain
secret but it would also infer that the no one else knew of your consultation Which is patently absurd since you would have had to book the appointment so the Practice manager/receptionist would also know as well as anyone else in the waiting room, so
Confidential would be a better word to describe that.
As I have just demonstrated, while
Private and
Secret may be synonyms (meaning describing similar things), a
Private meeting implies a quite different meaning from a
Secret meeting.
If you don't believe me then it's simple, try ringing your Surgery and ask for a
Secret appointment with your Doctor and see what happens.
It's context that always matters with words as it's what provides or implies a particular meaning to what is actually being described.
And as to what started this off and what you defended, I believe that writer deliberately changed the text from
Private to
Secret in an attempt to convey an element of furtiveness about the meeting and to thus fit in with his obsession of there being secretive Jewish control over things going on in the world ie NWO/PEZ bollocks.