I can happily accept that in certain cases the single right answer isn't ascertainable - there are limits to human epistemic prowess - but there is a single right set of possibilities - either the infantry withstand the charge, or they break - and this is disciplining the referee's decision to set some odds and call for the roll.
In the individual-level human behaviour cases, my view is that there is no single right set of possibilities, because where individual-level human behaviour is concerned that already admits indefinitely many possibilities. That's not to say anything goes - I think that most tables would accept that if Tanis meets Kitiara on the field of battle she's not going to rush up and offer him a rose - but the range of possibilities is very great - certainly more than two - and so there is no objective answer in that respect before we even get to the point of setting the odds.
I think this is what, in the history of RPG development, has driven (as a trend, not uniformally) character/theme-driven RPGing towards "say 'yes' or roll the dice", or similar sorts of approaches. (Ie I don't think this is just a coincidental convergence.) I'll try and explain why.
In the Waterloo example, there's also a sense in which there are indefinitely many possibilities - it's always possible that, right at that moment, an earthquake occurs and swallows up the infantry line, or a great wave sweeps them away (Belgium is a flat country, though Waterloo is a fair way inland, but hopefully you get my point), or whatever. But those possibilities are sufficiently remote and non-salient that the referee doesn't need to bother with them. The only salient possibilities are objectively ascertainable - holding or breaking.
In the Tanis-and-Kitiara example, how do we decide what the salient possibilities are, given the indefinite range of possible and plausible responses in human interaction? One way is GM chooses, which is the traditional way of running the DL modules. The other obvious way is that each participant in the play situation - player and GM - gets to nominate a salient possibility. The player puts forward his/hers, the GM puts forward his/hers. Then, when the dice are rolled, if the player wins his/her choice comes good; if the player loses the GM's choice comes good.
And this can be generalised to any situation in the game in which the inherent possibilities are multiple, but in which the player and GM can each fasten on one as the one s/he wants to put forward. It can handle not only Where can we find some sect members, where the player puts forward "In the teahouse" as their salient possibility, but even purely binary matters like Is there a secret door here? It seems that "yes" and "no" are the only possible options in this latter case, but if both are plausible then this can be resolved by the player opting for one, the GM the other, and making a check to see which is to be the case.
So I think it is the individual-level human-behaviour stuff - which is at the heart of character-driven play - that creates the impetus for "say 'yes' or roll the dice", but the method turns out to be easily generalised to all parts of the game, including doing "exploration" using the same dice-based resolution approach as we use for other elements of play, rather than relying on maps and notes as per the wargaming tradition. (In a Waterloo free kriegsspiel, rather than "Is there a secret door" one player might ask "Are their clouds"? I can imagine the referee rolling dice to determine the answer. But I think in free kriegsspiel that wouldn't be the default approach to establishing these "backstory" elements.)
And once exploration is done in that way, it too gets swallowed up into the theme stuff - if no one cares about secret doors than dice will never be rolled to determine whether or not there are any, but maybe the presence of curtains in rooms becomes a hot issue for that table for whatever reason. (Why do D&D maps and keys obsess over room height but not ceiling colour? I guess because we have a wall-climbing thief class, and rules for monster size and weapon length and the like, but no colour mage or interior decorator class. Given that we do have a druid class, why do D&D maps and keys not obsess over what plant life and (non-giant) vermin live in the dungeon? I guess because the druid is something of an ad hoc add on to the core dungeoneering game!)
In this way I think the move away from GM chooses for certain sorts of character-driven stuff leads to a more general move away from a wargame-type way of establishing setting and backstory to a much more "narrative"/"thematic" way of doing so. There's an inner logic to it, though obviously not every game has to travel all the way along the logical arrow.
).
