Taking the verb
rule literally, then my answer is No. No one has the power to issue an authoritative ruling of that sort. But as a member of the group, they can contribute to, perhaps take the lead in establishing, a conclusion that an attempted trait declaration is reaching.
But the player can establish the fictional position simultaneously with their declaration of the trait. Here's the example from the Scholar's Guide (pp 33-34):
Dro tells Thor, “I’ll hold off the gnolls while the rest escape.”
Thor inquires for more info, “What does Harguld do exactly?”
Dro says, “ I position myself inside the mouth of this cave, so I can see down the tunnel. Then I load my crossbow and take aim.”
Thor nods, “A gnoll scout emerges from the shadows down the tunnel…”
“I put a bolt in his face!”
“Right. Fighter skill test versus its Ambushing Nature 5.”
Dro announces, “I rolled three successes: 6, 4, 4”
Thor intones, “Three successes here…It’s a tie. What will you do, little dwarf?”
Dro could use his health 5 to make a tiebreaker roll against the gnoll. But he rolled one 6, so first he opts to spend a fate point to reroll that die hoping for another success. It comes up a 2. So now he has to choose to go to a tiebreaker roll or to use his trait against himself and break the tie in Thor’s favor.
After some consideration, he opts to break the tie in Thor’s favor. Dro declares, “I am so cunning! I wait for way too long trying to lure him in.” He used his Cunning trait to get in his own way and earns two checks for his trouble.
That is very obviously boxes-to-boxes - use of the Trait breaks the tie and grants Dro checks. And there is also a leftward arrow (ie to the clouds): Dro establishes that, in the fiction, Harguld has tried to be cunning, waiting for the gnoll to close in, and has misjudged his timing.
No fiction was established about the error of timing, or even the
importance of timing, prior to Dro introducing it as an output of the mechanical decision to use the trait.