It's not a style of play or a style of game. It's a mechanism for dealing with game failure when a player violates the social contract and acts dysfunctionally. The player doesn't want to face the consequences of their choices and has resorted to the metagame, implicitly with the threat of throwing a temper tantrum and ruining everyone's fun, and with a lot of GM wheedling possibly even bullying involved.
In such a situation, stopping the game to placate the jerk who has decided to try to 'win' by screwing the whole group over with invented gloves he gave not a thought about before learning the consequences is probably a better solution than letting that one little immature baby continue to derail the game.
But that's not a style of game. That is a concession to try to get the game going again instead of listening to an hour-long emotional rant by one player.
Note, this isn't the same as a legitimate GM mistake. If the character sheet says something like, "Gloves of Dexterity +2 (worn)" and the GM forgot to account for that fact, or if an hour earlier in the session the player had specifically said something like, "I put on my riding gloves and then dramatically bow to the baroness with a flourish of my cape" and nothing has happened to imply the gloves are now off, then the player has a point. The GM forgot part of the fiction (it happens) and should retcon his error.
But if the player says, "I was wearing gloves" off some flimsy pretense and doesn't have any evidence to back up that assertion and in fact has ignored the supposed gloves when grabbing gear or searching for secret doors, then "negotiating" isn't a style of game any more than a contested election is a style of government. We're negotiating here to prevent a rebellion, not because it's part of the agreed upon rules, and what that negotiation will look like - dice for it, partial concession, table vote, etc. - depends on things outside the game and nothing in the rule book.