By far the best way I’ve found to use the false Hydra so far is a week or two ahead of a session, to send out a link about the false Hydra to your group and be like “look at this neat monster I found!” Then present them with a story about people disappearing from a village and watch them invent their own false Hydra.
I’ve found that in general it doesn’t matter. If the party gets in their head that it’s a False Hydra, then they will typically ignore or justify the discrepancy.