Nnno, the modifiers I described in the post, where if one player wins a few dialogue rolls in a row, the other players get modifiers so they're more likely to win the next roll. And the longer a player goes without winning a roll, the bigger the modifier gets, so eventually a player that's been sidelined for long enough will be practically guaranteed to win. Nothing to do with stats at all.
That feels like it could possibly be manipulated? I do think that there should be some way for multiple players to be able to engage in a conversation but that system might be able to be abused to guarantee the passing of hard checks by purposefully making a player not engage so their bonus adds up, unless I am misunderstanding?