And that’s where the metagaming comes into play, with the player finding alternative ways to be able to act on what they believe was a lie, even though their character believes something to be a truth.

My favorite solution to this comes from Fate's compels. In short, you bribe the player with the equivalent of Inspiration for buying in.

So, yeah, maybe the NPC is lying, but I can invoke their "Very Trustworthy" aspect, because the dice said they're coming off as very trustworthy, and you get a nice shiny fate point so long as you go along with it.

It can channels the metagamer's desire to win in a more story friendly direction.