I'm not sure that a game that validates pemerton's proposed proposition actually exists, at least not in the form he suggests. Most games that have shared authorial control of the setting or backstory have some sort of rules framework that limits how much anyone other than the game moderator can introduce new setting or backstory elements. Typically these games grant players one or more variously described 'tokens' which must be spent (either put back in a pot or given to another participant) if you as a player are going to introduce new setting or backstory elements in author stance, and typically the other game participants can bid their own tokens to overrule the newly asserted element. No RPG I'm aware of allows as much arbitrary unlimited authorial control as pemerton's example of "Francis the Guard".
pemerton's hypothetical game where author insertions were valid player propositions at all times, would very likely cease to be an RPG and revert to a game of make-believe, as it would quickly degenerate toward the problem of no authorial control that RPGs were trying to solve with shared games of make-believe.
In other words, you might as well be playing "Cowboys & Indians" or "Cops & Robbers" where you have no mechanism for handling the mutually contradictory assertions, "I shot you!" and "No, you missed!"
If the player can propose on the fly a background that establishes or even overturns who a particular NPC is - whose to say that "Francis" doesn't already have a name and a stat block - what stops the following propositions from being valid:
a) "I notice that some has accidently dropped a wand of lightning bolts in the ditch!"
b) "My coming to this town fulfills a long awaited prophesy, and the inhabitants great me as their king, carry me on their shoulders, and shower me with gifts."
c) "When I was a youth, the goddess of death fell in love with me. As such, whomever I hate, she hates, and I am incapable of dying."
d) "Although I am a simple seeming rogue, for many years I was a secret student of the Grand College of the Archmagi, where I was a favored pupil that absorbed all that could be taught by the ancient masters. Now, recalling my long training and my great success their, I cast Polymorph Other to turn the dragon into a toad."
e) "My father was a master swordsmith so I pull out my +5 holy avenger which he gave to me as an heirloom."
Games of make believe can be fun, but they are not RPGs.
The fundamental problem that underlies this turn of discussion is that the truth of a backstory is expressed by and validated by the player's mechanical abilities. Backstory cannot be used to conjure abilities or resources out of thin air. You cannot assert new wealth, patrons, titles, rank, knowledge, allies or really any other sort of advantage on the basis of backstory. Backstory proceeds from and justifies the choices taken in character creation. You don't get to bypass character generation or other rules of the game just because backstory, nor can you reasonably introduce backstory to the game without consulting the rules (if the game allows for the possibility of found allies or resources, for example something like Mouseguard does with a Circles test) and the DM (as even with a circles test, the DM decides the obstacle to overcome). It's perfectly possible to create a backstory which cannot be expressed by character generation, but that doesn't mean that character generation is wrong and that you get all the resources you want simply because you wrote them down. Again, this is a player who isn't playing an RPG, but is engaged in playing "make believe".
