I've spoken to this before, coining the term "Avatar" vs. "Persona" playing.
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The biggest flaw (and many have pointed out) to Avatar play is that it reduces the character to a mere puppet.
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By contrast, Persona play has the problem of personality (and personality conflicts) can get in the way of the game. The classic "whats my motivation?" with characters come up, and inter-PC conflicts can derail the whole game.
Personally, I perfer Persona play. To the point that playing avatar play is akin to playing a video-game; I'm merely controlling a character rather than playing him.
In Forge terminology Persona is called "actor stance", but Avatar is distinguished between "Author stance" and "pawn stance". In Author stance, the player players the PC from outside rather than from within, but narrates the emotions/desires/etc of the PC so as to retroactively justify the decision made.
Assuming that everyone at the table is agreed that pawn stance is bad (because it's not really roleplaying, and we're all here to play an RPG, right!), then any challenge to the character is also a challenge to an author-stance player, because the player has to come up with an ingame rationale for the behaviour of her PC which is satisfactory to the rest of the table. Interestingly, though, the challenge to the player is not the same as the challenge to the PC - it is a sort of metagame challenge, to come up with a good story.
If a player has adopted Persona/actor stance, then any challenge to the character may or may not be a challenge to the player, depending on what device is used to work out the character's response to the challenge - game mechanics unmediated by player choices (eg I roll my to hit, I roll my diplomacy skill, etc) don't challenge the player, but once those game mechanics require the player to make choices (eg I choose to charge, drawing the AoA from X so I can flank Y) then the player will be challenged as well as the character. The more simulationist the mechanics, the more the challenge to the player will be the same sort of challenge as that faced by the character (eg a tactical challenge).
I agree with Cadfan that an interesting game, even one that is intended to be played in actor/Persona stance, benefits from requiring interesting choices of the player, rather than just roll, roll, roll . . .
I also think that it is a mistake to confuse the issue of challenging the player vs challenging the PC with a quite different issue, which is whether the action resolution mechanics should be highly structured with an important role for mathematics and/or dice, or rather should be based primarily on a players' ability to spin a plausible tale of why her PC succeeds. It seems that most people prefer some version of the structured approach for combat, but that there is a signficant split over whether social conflict should be resolved using maths and dice (eg as in 4e's skill challenges or HeroWars's extended contests) or via player tale-spinning ("Here's what I say to the Duke . . . pretty persuasive, wasn't it!").
You might be misunderstanding me: I'm saying that Bob is helping Mike come up with Verys' answer, because it's Verys who is supposed to be the eloquent one, not Dumb Krunk, who is the Dwarf Battlerager that Bob is playing. So if that sphinx is asking only Verys, Bob is contributing, too, because Verys is smarter than both of them put together, on paper.
If Verys asks for help or somehow gets the rest of the party involved, then well and good. But if s/he doesn't, and the rest of the party don't know what's going on (let's say only Verys can understand the Sphinx) then help from the other players (in or out of character) gets smacked down fast and hard.
I tend to prefer Henry's approach. But given that it obviously involves metagame thinking, it fits better with an author-stance rather than an actor-stance approach to playing one's PC.
However, if Bob can help Verys with the Sphinx, it's a pretty short slide down the slope to have Bob "help" Verys in other ways; in other words, you can quickly end up with people part-playing characters not their own. And that, believe me, gets messy.
I've never had this problem, but I can imagine that it could be a problem. I think if the general approach of a group was actor/Persona stance rather than author/(motivated-)Avatar stance, then the problem could come up more readily, as it would become ambiguous who was the "actor" for Verys - whereas multiple authorship doesn't threaten a particular PC's ownership of Verys in the same way, as it would still be that player who, after the metagame discussion has come to an end, would actually make the final call as to what Verys does/says.