Yes, I understood that. By
the table's understanding I meant
the table's understanding of what's in and out of the bounds of good taste etc.
As I posted, I think that the idea is that (i)
because the GM is, in virtue of his/her participant role, especially attentive to the content of the fiction and the implications for that of action declarations - and (ii)
because the GM is the person expected to speak next after a player declares an action, therefore (iii)
the GM has a special opportunity, compared to other participants, to nip egregious action declarations in the bud.
So I don't see it - at least
@Don Durito's version - as an argument for, or appeal to, and special
authority that the GM enjoys; but rather as an appeal to a special
capacity that the GM enjoys in virtue of the dynamics of play (i) and (ii). To the extent that (i) and (ii) don't hold - eg everyone is equally attentive to the fiction and thinking through the implications for it of individual action declarations (perhaps more common at "serious" than "casual" tables), and non-GM participants routinely engage with one another about their action declarations (perhaps more common among friends than eg at a pick-up game) - then there would be no special capacity and so (iii) wouldn't follow.
I don't know if Don Durito (or other posters) have pick-up/game-store type games in mind, but as my bit inside the dashes in the previous paragraph hints at, I think these are more likely to be situations where the GM gets that special opportunity, because more likely to be "casual" and less likely to have robust "horizontal" interaction among non-GM participants.