How can any estimate, even a very poor estimate, be not genuine if there isn't a known better estimate? If I estimate there are 8 alien civilizations in the milky way it may be a truly terrible estimate, and the methods by which I came up with that estimate (eg one per galactic arm) may not stand up to any rigorous scrutiny, but it's as genuine an estimate as any other. To be not genuine, there must be something that is genuine, which it is not.

You don't need to necessarily know the right answer to have a fake estimate, but you have to be doing something to the estimate that you know is making it worse, which is equivalent to having the estimate where you didn't do that, which would be better.