Celebrim
Legend
And, as I have a moment more to go back to this post and discuss your conjecture that such a game would devolve. This is actually well discussed as the Czerge Principle, and comes in when a player can both set the problem and propose the solution. It's most often avoided in games that allow the players the latitude to make such declarations by the reason you cite for Mouseguard -- the DM sets up the obstacles and the players' attempted solutions are tested. I find it interesting that you're familiar with Mouseguard to this extent but don't recognize a Circles test in [MENTION=42582]pemerton[/MENTION]'s example. I haven't played MG or BW, but I could easily see the Circles test lurking.
If D&D had anything like circles that a player had to spend resources for in chargen in order to obtain the advantage of, then sure, then sure. You have some sort of reasonable check and balance on the claim, including, as in Mousegaurd, that the GM can set the OB of the test. What bother's me about pemerton's example is less that you might test something not established in the myth, but that a player might try to invent background on the fly to justify overcoming an obstacle. In Mousegaurd, for example, you have character burner that very tightly establishes the limits of your character - where he is from and who he grew up with - which in turn means that the 'circle' of your circles test is delimited by your background. You can make circles tests in Mousegaurd precisely because the myth of your character is a pretty stable and knowable, and we can make inferences as to when it really is reasonable that you might know someone.
I should also tell you that for the last few months, I've been having a running debate with myself over which is the worst designed RPG - Mouseguard or RIFTS. Mousegaurd is the first thing I've tried to play that even comes close enough to be in such a debate.
There is a core of a great game somewhere in Mousegaurd, and there is a huge amount of imagination and creativity involved, but wow are the rules poorly thought out.