I never said that. Let me explain it to you with an example:
15 year old comes to his father (in NY) and says: can I go to EY?
Father responds: You may go, but you can't travel by plane, train, ship, car or bus.
Did the father allow his son to go to EY? Did he say one thing but mean something else?
Given that the Rebbe didn't just say no, as he wasn't afraid to do in many other cases, the onus is still on you to prove that the Rebbe was using a very rare usage of hyperbole to reject all of the eruvim when he replied to make them in secret in order to prevent the transgression of carrying on Shabbos without an eruv.
The same onus applies if you want to suggest that the Rebbe's written replies for cities like Manhattan and Melbourne were not hyperbole and that only the CH eruv was hyperbole.
Your argument that the Rebbe never said this for CH has already been proven wrong.
Your "proof" that in CH an eruv can't be erected in secret has also been proven wrong.