Coming to “agreement” over a fiction isn’t okay. No amount of rationalization makes it “business”. More to the point, it is unnecessary. I hold there is harm here.
A different skillset is needed to negotiate from truth (“we need to confer with our building teams to estimate the full project timeline”) and still be persuasive. It’s not more difficult, and these these skills are not rare. They don’t get used in some environments (not many, certainly not most) because of culture, and at the ultimate expense of the leaders that set it.