Fake simply means not genuine. It doesn’t require the people reporting it to have a real estimate. It simply requires the people reporting it to just not try finding the real number.
I'm trying to think of a definition, and the best I can come up with is this: fake means the number was modified at some point without an auditable trail. For example, if I see 1 deer on a sq km and I extrapolate linearly to a 100 sq km area that there are 100 deer in that area, then the number is fake if I don't disclose the extrapolation -- and this is true even if the actual number is in fact 100 in reality.
Actually, I don't even think this covers all the bases, because it assumes there was an initially factual measurement. For example, if it that one observed deer was in fact a statue, the numbers are all fake even if everyone documented everything and acted in good faith and accidentally came up with true correct number at the end...