Not even that. If I give you a fake number (by whatever definition) and you report it... the number is still fake, regardless of whether you had any inkling it might be, or whether you tried to verify it in any way.

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...